Solve the linear system.

Slides:



Advertisements
Similar presentations
Use addition to eliminate a variable
Advertisements

SOLUTION EXAMPLE 1 Multiply one equation, then add Solve the linear system: 6x + 5y = 19 Equation 1 2x + 3y = 5 Equation 2 STEP 1 Multiply Equation 2 by.
Standardized Test Practice EXAMPLE 3 Darlene is making a quilt that has alternating stripes of regular quilting fabric and sateen fabric. She spends $76.
Write a system of equations. Let x represent
Rational Expressions To add or subtract rational expressions, find the least common denominator, rewrite all terms with the LCD as the new denominator,
Algebra 7.3 Solving Linear Systems by Linear Combinations.
Solve an equation with variables on both sides
Directions: Solve the linear systems of equations by graphing. Use the graph paper from the table. Tell whether you think the problems have one solution,
Solve an absolute value equation EXAMPLE 2 SOLUTION Rewrite the absolute value equation as two equations. Then solve each equation separately. x – 3 =
TODAY IN ALGEBRA…  Warm Up: Solving a system by Elimination  Learning Goal: 7.4 You will solve systems of linear equations by Elimination with multiplication.
Write decimal as percent. Divide each side by 136. Substitute 51 for a and 136 for b. Write percent equation. Find a percent using the percent equation.
Do Now Pass out calculators. Solve the following system by graphing: Graph paper is in the back. 5x + 2y = 9 x + y = -3 Solve the following system by using.
Solving Systems of Linear Equations
Solving Linear Systems by Linear Combinations
Unit 3 – Chapter 7.
Examples and Guided Practice come from the Algebra 1 PowerPoint Presentations available at
Warm Up Simplify each expression. 1. 3x + 2y – 5x – 2y
Warm-Up Exercises 1. 2m – 6 + 4m = 12 ANSWER 6 Solve the equation. 2.6a – 5(a – 1) = 11 ANSWER 3.
Goal: Solve a system of linear equations in two variables by the linear combination method.
Solving Linear Systems Using Linear Combinations There are two methods of solving a system of equations algebraically: Elimination (Linear Combinations)
Solve an absolute value equation EXAMPLE 2 SOLUTION Rewrite the absolute value equation as two equations. Then solve each equation separately. x – 3 =
KAYAKING EXAMPLE 4 Write and solve a linear system During a kayaking trip, a kayaker travels 12 miles upstream (against the current) and 12 miles downstream.
Warm-Up Exercises 1. Use the quadratic formula to solve 2x 2 – 3x – 1 = 0. Round the nearest hundredth. 2. Use synthetic substitution to evaluate f (x)
Lesson 6-4 Warm-Up.
Warm Up Simplify each expression. 1. 3(10a + 4) – (20 – t) + 8t 3. (8m + 2n) – (5m + 3n) 30a t 3m – n 4. y – 2x = 4 x + y = 7 Solve by.
Use the substitution method
Solve Linear Systems by Substitution January 28, 2014 Pages
6.2 Solve a System by Using Linear Combinations
Solve Linear Systems by Substitution Students will solve systems of linear equations by substitution. Students will do assigned homework. Students will.
Multiply one equation, then add
Solve Linear Systems by Elimination February 3, 2014 Pages
2.2 Solve One-Step Equations You will solve one-step equations using algebra. Essential Question: How do you solve one- step equations using subtraction,
LAB: Inequalities with Negative Coefficients p.304 Q U E ST ION: How do you solve an inequality with a negative coefficient?
WARM-UP. SYSTEMS OF EQUATIONS: ELIMINATION 1)Rewrite each equation in standard form, eliminating fraction coefficients. 2)If necessary, multiply one.
Solving Systems by Elimination
Rewrite a linear equation
Solve Linear Systems By Multiplying First
1. Solve the linear system using substitution.
Solve the linear system.
Add and Subtract Rational Expressions
EXAMPLE 2 Rationalize denominators of fractions Simplify
Solve the linear system.
5.3 Solving Systems of Linear Equations by Elimination
Solve for variable 3x = 6 7x = -21
Solve an equation by multiplying by a reciprocal
3.1 Solving Two-Step Equations
11.3 Solving Linear Systems by Adding or Subtracting
Warm Up Simplify each expression. 1. 3x + 2y – 5x – 2y
Lesson Objectives: I will be able to …
5.3 Solving Systems of Linear Equations by Elimination
REVIEW: Solving Linear Systems by Elimination
Solve Systems of Equations by Elimination
Lesson 7.4 Solve Linear Systems by Multiplying First
Warm Up Lesson Presentation Lesson Quiz
Solve an equation by combining like terms
Solving Systems Check Point Quiz Corrections
Before: December 4, 2017 Solve each system by substitution. Steps:
Objectives Solve systems of linear equations in two variables by elimination. Compare and choose an appropriate method for solving systems of linear equations.
Notes Solving a System by Elimination
Notes Solving a System by Elimination
Solving one- and two-step equations
Solving One Step Equations
Solving Systems by Elimination
Warmup Solve the following system using SUBSTITUTION:
Example 2B: Solving Linear Systems by Elimination
Solving Systems of Equations by Multiplying First - Elimination
3.1 Solving Two-Step Equations 1 3x + 7 = –5 3x + 7 = –5 – 7 – 7
Warm Up.
The Substitution Method
Presentation transcript:

Solve the linear system. 1. 4x – 3y = 15 2x – 3y = 9 ANSWER (3, –1) 2. –2x + y = –8 2x – 2y = 8 ANSWER (4, 0)

3. You can row a canoe 10 miles upstream in 2 3. You can row a canoe 10 miles upstream in 2.5 hours and 10 miles downstream in 2 hours. What is the average speed of the canoe in still water? ANSWER 4.5 mi/h

Multiply one equation, then add EXAMPLE 1 Multiply one equation, then add Solve the linear system: 6x + 5y = 19 Equation 1 2x + 3y = 5 Equation 2 SOLUTION STEP 1 Multiply Equation 2 by –3 so that the coefficients of x are opposites. 6x + 5y = 19 6x + 5y = 19 2x + 3y = 5 –6x – 9y = –15 STEP 2 Add the equations. –4y = 4

Multiply one equation, then add EXAMPLE 1 Multiply one equation, then add STEP 3 Solve for y. y = –1 STEP 4 Substitute –1 for y in either of the original equations and solve for x. 2x + 3y = 5 Write Equation 2. 2x + 3(–1) = 5 Substitute –1 for y. 2x + (–3) = 5 Multiply. 2x = 8 Subtract –3 from each side. x = 4 Divide each side by 2.

Multiply one equation, then add EXAMPLE 1 Multiply one equation, then add ANSWER The solution is (4, –1). CHECK Substitute 4 for x and –1 for y in each of the original equations. Equation 1 Equation 2 6x + 5y = 19 2x + 3y = 5 6(4) + 5(–1) = 19 ? 2(4) + 3(–1) = 5 ? 19 = 19 5 = 5

Multiply both equations, then subtract EXAMPLE 2 Multiply both equations, then subtract Solve the linear system: 4x + 5y = 35 Equation 1 2y = 3x – 9 Equation 2 SOLUTION STEP 1 Arrange the equations so that like terms are in columns. 4x + 5y = 35 Write Equation 1. –3x + 2y = –9 Rewrite Equation 2.

EXAMPLE 2 Multiply both equations, then subtract STEP 2 Multiply Equation 1 by 2 and Equation 2 by 5 so that the coefficient of y in each equation is the least common multiple of 5 and 2, or 10. 4x + 5y = 35 8x + 10y = 70 –3x + 2y = –9 –15x +10y = –45 STEP 3 Subtract: the equations. 23x = 115 STEP 4 Solve: for x. x = 5

Multiply both equations, then subtract EXAMPLE 2 Multiply both equations, then subtract STEP 5 Substitute 5 for x in either of the original equations and solve for y. 4x + 5y = 35 Write Equation 1. 4(5) + 5y = 35 Substitute 5 for x. y = 3 Solve for y. ANSWER The solution is (5, 3).

Multiply both equations, then subtract EXAMPLE 2 Multiply both equations, then subtract CHECK Substitute 5 for x and 3 for y in each of the original equations. Equation 1 Equation 2 4x + 5y = 35 2y = 3x – 9 4(5) + 5(3) = 35 ? 2(3) = 3(5) – 9 ? 35 = 35 6 = 6 ANSWER The solution is (5, 3).

GUIDED PRACTICE for Examples 1 and 2 Solve the linear system using elimination. 6x – 2y = 1 1. –2x + 3y = –5 ANSWER The solution is (–0.5, –2).

GUIDED PRACTICE for Examples 1 and 2 Solve the linear system using elimination. 2x + 5y = 3 2. 3x + 10y = –3 ANSWER The solution is (9, –3).

GUIDED PRACTICE for Examples 1 and 2 Solve the linear system using elimination. 3x – 7y = 5 3. 9y = 5x + 5 ANSWER The solution is (–10, –5).

EXAMPLE 3 Standardized Test Practice Darlene is making a quilt that has alternating stripes of regular quilting fabric and sateen fabric. She spends $76 on a total of 16 yards of the two fabrics at a fabric store. Which system of equations can be used to find the amount x (in yards) of regular quilting fabric and the amount y (in yards) of sateen fabric she purchased? x + y = 16 A x + y = 16 B x + y = 76 4x + 6y = 76 x + y = 16 D x + y = 76 C 4x + 6y = 16 6x + 4y = 76

EXAMPLE 3 Standardized Test Practice SOLUTION Write a system of equations where x is the number of yards of regular quilting fabric purchased and y is the number of yards of sateen fabric purchased. Equation 1: Amount of fabric x + y = 16

Standardized Test Practice EXAMPLE 3 Standardized Test Practice Equation 2: Cost of fabric 4 76 6 + = y x The system of equations is: x + y = 16 Equation 1 4x + 6y = 76 Equation 2 ANSWER A D C B The correct answer is B.

GUIDED PRACTICE for Example 3 SOCCER A sports equipment store is having a sale on soccer balls. A soccer coach purchases 10 soccer balls and 2 soccer ball bags for $155. Another soccer coach purchases 12 soccer balls and 3 soccer ball bags for $189. Find the cost of a soccer ball and the cost of a soccer ball bag. 4. ANSWER soccer ball $14.50, soccer ball bag: $5

Daily Homework Quiz Solve the linear system using elimination. 1. 8x + 3y = 12 –2x + y = 4 ANSWER (0, 4) 2. –3x + 2y = 7 5x – 4y = –15 ANSWER (1, 5) 3. –7x – 3y = 11 4x – 2y = 16 ANSWER (1, –6)

Daily Homework Quiz A recreation center charges nonmembers $3 to use the pool and $5 to use the basketball courts. A person pays $42 to use the recreation facilities 12 times. How many times did the person use the pool. 4. ANSWER 9 times