1. Solving systems using substitution

2. Three methods to solving systems
1) Graphing
2) Elimination
3) Substitution

3. The purpose of substitution
To substitute for one of the variables, so that you
only have 1 variable to solve for.

4. Substitution Basics 4(3) + 2 = 14 4(x) + 2 = 4x + 2
4Y + 2
4(3) + 2 = 14
Y = 3
4(x) + 2 = 4x + 2
Y = X
4(x+2) + 2 = 4x + 10
Y = (x + 2)

5. y = 4x
3x + y = -21
Notice that one of the equations is solved for Y. So we can
Replace Y in the other equation with __________ 4x
3x + y = -21
3x + 4x = -21
Now we can solve for x.
7x = -21
X = -3

6. y = 4x 3x + y = -21 Now that we know X = -3 . We can solve for Y.
Solution to the system is (-3, -12).

7. y = 4x 3x + y = -21 3x + y = -21 y = 4x 3(-3) + (-12) = -21
Check the solution in both equations.
Solution to the system is (-3,-12).
3x + y = -21
3(-3) + (-12) = -21
-9 + (-12) = -21
-21= -21
y = 4x
-12 = 4(-3)
-12 = -12

8. x + y = 10
5x – y = 2
Neither of the equations is solved for x or y, so you will
Need to solve one of the equations for x or y.
X = 10 – Y or
Y = 10 - X
You choose which one you want. For right now we are
Going to choose to use x = 10-Y

9. x + y = 10 5x – y = 2 Substitute x = 10 – y in the second equation
5(10-y) –y = 2
50 -5y – y = 2
50 -6y = 2
-6y = -48
Y = 8

10. Solution to the system is (2,8).
x + y = 10
5x – y = 2
Now that we know that Y = 8 we can solve for X
X + 8 = 10
X = 2
Solution to the system is (2,8).

11. 5x – y = 2 x + y =10 5(2) - (8) = 2 2 + 8 =10 10 – 8 = 2 10 =10 2 = 2
Check the solution in both equations.
Solution to the system is (2, 8).
5x – y = 2
5(2) - (8) = 2
10 – 8 = 2
2 = 2
x + y =10
2 + 8 =10
10 =10

12. Solve by substitution:1. 2.
Solve by substitution: