Mrs. Brown Maternity Leave 8Th Grade Week 6 Mrs. Brown Maternity Leave

Day1: Review Systems A system of equations is two linear equations in which the one point is the solution. This point is where both line meet or intersect. For Example: Y=3x+1 7= 3(2)+1 7=7 Y=2x+3 7= 2(2)+3 7=7 (2,7) is the solution to the system because it makes both equations true.

Graphing to Solve One method to solve a system is to graph both equations and find the point of intersection.

Standard Form: Convert then graph

Practice Worksheet All practice work may be done with your partner and with a calculator. If you are not behaving and focusing on the math, this privilege may be taken away by the teacher.

Day 2: Solving with Elimination When you solve with elimination or combination method you can combine two variables so that they cancel or eliminate. The solve for the remaining variable. Then use that value to solve for the other variable. Remember the answer to every system is an X and Y value!

Example:

Example Some times you will have to multiply one of the equations in order to make them able to eliminate. 2x+3y=10 2x+3y =10 x+y=6 -2(x+y=6) -2x+ -2y=-12 Now we can eliminate and solve! Y= -2 2x+3(-2)=10 2x+-6=10 solution(8, -2) 6 6 2x=16 x=8

EX: Multiply both equations !!

Practice: Worksheet All practice work may be done with your partner and with a calculator. If you are not behaving and focusing on the math, this privilege may be taken away by the teacher.

Day 3: systems with substitution When using substitution you need to have a variable alone in one of the equations. Then substitute that entire expression into the other equations and solve for the variable. Then you can use that value to substitute in and solve for the unknown variable. Remember you need an x and y value for every system!

Example Here they tell you the value of x! So, you only have to solve for the value of y and you are done!

Example Here they give you y= x+1, so they put that entire expression in for y in the other equation and solve. Then they use the x value to solve for y! Done!

Some time you may have to get a variable alone before sub.

Practice: Worksheet All practice work may be done with your partner and with a calculator. If you are not behaving and focusing on the math, this privilege may be taken away by the teacher.

Day 4: infinite or no solution systems Just like in multi step equations there may be a system with infinite solutions or no solution. Infinite solutions will have the same exact slope and y intercept. Which result in both equations actually being the same line. This mean that any values will make both equations true. No solution means that the lines will never meet they will have different intercepts and the same slope. Therefore no values will fit both.

Infinite when graphing Convert both Equations to y= X-2y=-2 -x -x -2y= -x-2 y= 1/2x+1 -2 -2 -2x +4y =4 2x 2x 4y=2x+4 y= 1/2x+1 4 4 They are the exact same!

No solution when graphing

Infinite solution: elimination -8x-6y=-12 4x+3y= 6 Multiply the second equation by 2: 8x+6y=12 8x+6y=12 0=0 infinite solutions!

No solution with Elimination 9x+6y=14 -3x-2y= 6 Multiply the second equation by 3: -9x-6y=18 -9x-6y=18 0 = 32 No Solution!

No solution with Sub. When we substitute the equation in a solve, the side are not equivalent: NO Solution!

Infinite solution with substitution In this example when we plug in the equations we get the same thing on each side!

Practice Worksheet All practice work may be done with your partner and with a calculator. If you are not behaving and focusing on the math, this privilege may be taken away by the teacher.

Day 5: Quiz Use your packet of notes to complete the quiz. You have 40 minutes. There are NO RETAKES for open note quizzes!!!