5D Solve by Substitution
1.
2.
3.
4.
5.
Find one variable that be solved for easily.
Solve for that one variable <isolated equation>
Substitute using ( ) for that variable into the other equation
Solve for the other variable.
Plug the found variable into the isolated equation in #2 to find the 2nd variable.
Example 1
(A) 5x + y = 2
(B) 2x – 6y = 20
It’s easy to isolate the y in (A).
(Isolated A) y = -5x + 2
Now substitute into (B) replacing the y.
(B) 2x – 6(-5x + 2) = 20
2x + 30x – 12 = 20
32x – 12 = 20
32x = 32
x=1
Now plug into (Isolated A)
y = -5(1) + 2
y = -5 + 2
y = -3
(1,-3)
Example 2
(A) 2x – 6y = 18
(B) -x – 2y = 1
It’s easy to isolate the x in (B)
(Isolated B) -x = 1 + 2y  x = -1 – 2y (divide by -1)
Now substitute into (A) replacing the x.
(A) 2(-1 – 2y) – 6y = 18
-2 – 4y – 6y = 18
<distribute>
-2 - 10y = 18
<simplify>
-10y = 20
<add 2 to both sides>
y = -2
<divide by -10>
Now plug into (Isolated B)
x = -1 – 2(-2)
x = -1 + 4
x=3
(3,-2)
 If both variables disappear then the answer is either no solution (0 = #) or infinitely many (0= 0)
Example 3
Example 4
2(3 – x) + 2x = 13
5(3 – y ) + 5y = 15
6 – 2x + 2x = 13
15 – 5y + 5y = 15
6 = 13
15 = 15
0 = 7 No solution
0 = 0 Infinitely many
O: Fill in the blanks:
3x + 2y = 10
3(3y + 7)+2y = 10
x = 3y+ 7
9y + _____ + 2y = 10
____+21 = 10
11y = -11
y = -1
x = 3y + 7
x = 3( ) + 7
x=
1-4: Isolate the variable that is easiest to isolate
1. 2x + y = 12
2. 2y – x = 12
5x – 3y = 16
10y + 3x = 15
3. 2x + 4y = 12
x + 3y = 11
4. 2x – 3y = 12
5x – y = 15
5-12: Solve by substitution
5. x + 2y = 11
6. y = 12 – 4x
3x – 7y = -32
5x – 3y = -2
7. 9x – 3y = 18
x + 2y = -12
8. 4x – 3y = -14
2x – y = -4
9. 3x + 5y = 14
x = 3y
10. x + 2y = 10
2x + 4y = 20
11. 2x – 4y = 4
5x – y = 28
12. 2x – y = 10
6x – 3y = 12
13-16: Identify which is a better method (substitution or elimination) and then solve using that
method
13. 2x + 4y = 10
14. y = 3x + 2
15. 3x – 4y = 16
16. m = 2n
3x – 4y = -5
2x – 3y = -41
2x + 5y = 3
m + n = 18
17. Bob’s is twice as old as Sally. Their combined ages is 36. How old is Bob?
18. The perimeter of a rectangle is 40. The length is four less than twice the width. What are the dimensions
of the rectangle?
19. The price of soda is $0.50 more than the price of a bag of chips.
of chips and paid $12.50. How much is a bag of chips?
20. Solve for y:
A. 4
B. 1
3x + 2y = 10
y = -x + 3
C. -1 D. -1
Juan bought three sodas and four bags
21. Charles is five times as old as Mary. Their
combined ages is 36. How old is Charles?
A. 6
B. 12
C. 30
D. 36