1. Solving Systems of Equations using Substitution
Unit 2
Lesson 2

2. Warm-Up Explain what the solution to a system of equations is.
A point or (x, y) pair that works for EVERY equation of the system!!

3. Essential Question
What are the advantages and disadvantages of solving a system of equations algebraically rather than by using a graph or table?

4. Solving Systems of Equations using Substitution
Steps:
Solve one equation for one variable (y= ; x= ; a=)
TIP: pick the easiest variable (the “1x” or “1y”)
2. Substitute the expression from step one into the other equation and solve.
3. Use that value in the first equation to solve for the
2nd variable.
4. Check your answer in both ORIGINAL equations of
the system.
5. Write your solution as an ordered pair. ( ?, ?)

5. Example #1:
y = 4x
3x + y = -21
Step 1: Solve one equation for one variable.
y = 4x (This equation is already solved for y.)
Step 2: Substitute the expression from step one into the other equation.
3x + y = -21
3x + 4x = -21
Simplify and solve the equation.
7x = -21
x = -3

6. y = 4x 3x + y = -21 Step 3: Substitute back into either original
equation to find the value of the other
variable.
3x + y = -21
3(-3) + y = -21
-9 + y = -21
y = -12
Solution to the system appears to be
the point (-3, -12).
Now check your answer!

7. y = 4x 3x + y = -21 3x + y = -21 y = 4x 3(-3) + (-12) = -21
Step 4: 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. Example #2: x + y = 10 y = -x +10 5x - y = 2 5x -(-x +10) = 2
Step 1: Solve one equation for one variable.
x + y = 10
y = -x +10
Step 2: Substitute the expression from step one into
the other equation.
5x - y = 2
5x -(-x +10) = 2

9. 5x -(-x + 10) = 2 5x + x -10 = 2 6x -10 = 2 6x = 12 x = 2 x + y = 10
Step 3: Simplify and solve the equation.
5x -(-x + 10) = 2
5x + x -10 = 2
6x -10 = 2
6x = 12
x = 2

10. Solution to the system is (2,8).
x + y = 10
5x – y = 2
Step 4: Substitute back into either original
equation to find the value of the other
variable.
x + y = 10
2 + y = 10
y = 8
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
Step 5: 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.