Download presentation
Presentation is loading. Please wait.
Published byVanessa Pope Modified over 8 years ago
1
Chapter 7.3
2
Objective NCSCOS 4.03 Students will know how to solve a system of equations using addition
3
What is a system of equations? Two equations where we try and find their intersection.
4
What are the possible solutions to a system of equations? One solution – an ordered pair where the two lines intersect No solution – the lines are parallel so they have no points of intersection Infinitely many solutions – they are the same line so every point on one line is the same as the other line
5
Example 1: Use addition to solve the system of equations:
6
To solve a system of equations we have to eliminate one of the variables If we were to add these together could we eliminate one of the variables? Yes, the y’s add up to zero! We can add the equations together to “get rid” of the y’s
7
We add the equations x + 3x = 4x -3y + 3y = 0 We don’t write 0y so it goes away 7 + 9 = 16
8
Solve for x Divide both sides by 4 4 is the x value in the point where the two lines intersect
9
Once you know x, plug it into either equation to find the y value We’ll use the first one
10
Substitute 4 for x Subtract 4 from both sides Divide by -3 -1 is the y value for the point where the 2 lines intersect
11
Example 1: Use addition to solve the system of equations: The solution to this problem is the point where they intersect The answer is:
12
Solve the following system of equations 1. x – 2y = 4 2x + 2y = 2 3. 2x – 5y = -4 4x + 5y = -8 5. -6x + 4y = -10 2x – 4y = -2 4. -3x – 2y = 4 2x + 2y = -2 2. x + 4y = 3 3x – 4y = -7
13
Solve the following system of equations 1. x – 2y = 4 2x + 2y = 2 3. 2x – 5y = -4 4x + 5y = -8 5. -6x + 4y = -10 2x – 4y = -2 4. -3x – 2y = 4 2x + 2y = -2 2. x + 4y = 3 3x – 4y = -7 1.(2, -1) 2. (-1, 1) 3. (-2, 0) 4. (-2, 1) 5. (3, 2)
14
Example 2: Solve the following system of equations: Does it matter which variable I solve for first? No!
15
This problem we will have to solve for y first since the x’s add up to zero Add the two equations Divide by 3
16
Plug the y value into either equation Solve for x
17
Solve the following system of equations: 1. -x + 3y = 7 x + y = -1 3. -4x + 2y = 2 4x – 2y = 4 4. 3x + 2y = 9 -3x – 8y = 3 5. -2x + 3y = -2 2x – 6y = -4 2. -2x + 3y = 7 2x – 4y = -3
18
Solve the following system of equations: 1. -x + 3y = 9 x + y = -1 3. -4x + 2y = 2 4x – 2y = 4 4. 3x + 2y = 8 -3x – 8y = 4 5. -2x + 3y = -2 2x – 6y = -4 2. -2x + 3y = 8 2x – 4y = -4 1.(-3, 2) 2.(-10, -4) 3.No Solution 4.(4, -2) 5.(4, 2)
Similar presentations
© 2024 SlidePlayer.com. Inc.
All rights reserved.