SUBSTITUTION METHOD WORKSHEET
Substitution Method Worksheet :
Worksheet given in this section will be much useful for the students who would like to practice problems on solving system of equations by substitution.
Before look at the worksheet, if you would like to learn how to solve system of equations by substitution,
Substitution Method Worksheet - Problems
Problem 1 :
Solve for x and y :
x - 5y + 17 = 0
2x + y + 1 = 0
Problem 2 :
Solve for x and y :
5x + 3y - 8 = 0
2x - 3y + 1 = 0
Problem 3 :
Solve for x and y :
4x - 7y = 0
8x - y - 26 = 0
Problem 4 :
Solve for x and y :
3x + 5y - 6 = 0
5x - y - 10 = 0 = 0
Problem 5 :
Solve for x and y :
2x + 3y = 5
3x + 4y = 7
Substitution Method Worksheet - Solutions
Problem 1 :
Solve for x and y :
x - 5y + 17 = 0
2x + y + 1 = 0
Solution :
x - 5y + 17 = 0 -----(1)
2x + y + 1 = 0 -----(2)
Step 1 :
Solve (1) for x.
x - 5y + 17 = 0
Subtract 17 from each side.
x - 5y = -17
Add 5y to each side.
x = 5y - 17 -----(3)
Step 2 :
Substitute (5y - 17) for x into (2).
(2)-----> 2(5y - 17) + y + 1 = 0
10y - 34 + y + 1 = 0
11y - 33 = 0
Add 33 to each side.
11y = 33
Divide each side by 11.
y = 3
Step 3 :
Substitute 3 for y into (3).
(3)-----> x = 5(3) - 17
x = 15 - 17
x = -2
Therefore, the solution is
(x, y) = (-2, 3)
Problem 2 :
Solve for x and y :
5x + 3y - 8 = 0
2x - 3y + 1 = 0
Solution :
5x + 3y - 8 = 0 -----(1)
2x - 3y + 1 = 0 -----(2)
Step 1 :
Solve (1) for 3y.
5x + 3y - 8 = 0
Add 8 to each side.
5x + 3y = 8
Subtract 5x from each side.
3y = 8 - 5x -----(3)
Step 2 :
Substitute (8 - 5x) for 3y into (2).
(2)-----> 2x - (8 - 5x) + 1 = 0
2x - 8 + 5x + 1 = 0
7x - 7 = 0
Add 7 to each side.
7x = 7
Divide each side by 7.
x = 1
Step 3 :
Substitute 1 for x into (3).
(3)-----> 3y = 8 - 5(1)
3y = 8 - 5
3y = 3
Divide each side by 3.
y = 1
Therefore, the solution is
(x, y) = (1, 1)
Problem 3 :
Solve for x and y :
4x - 7y = 0
8x - y - 26 = 0
Solution :
4x - 7y = 0 -----(1)
8x - y - 26 = 0 -----(2)
Step 1 :
Solve (1) for 4x.
4x - 7y = 0
Add 7y to each side.
4x = 7y -----(3)
Step 2 :
Substitute 7y for 4x into (2).
(2)-----> 8x - y - 26 = 0
2(4x) - y - 26 = 0
2(7y) - y - 26 = 0
Simplify.
14y - y - 26 = 0
13y - 26 = 0
Add 26 to each side.
13y = 26
Divide each side by 13.
y = 2
Step 3 :
Substitute 2 for y into (3).
(3)-----> 4x = 7(2)
4x = 14
Divide each side by 4.
x = 3.5
Therefore, the solution is
(x, y) = (3.5, 2)
Problem 4 :
Solve for x and y :
3x + 5y - 6 = 0
5x - y - 10 = 0 = 0
Solution :
3x + 5y - 6 = 0 -----(1)
5x - y - 10 = 0 -----(2)
Step 1 :
Solve (2) for y.
5x - y - 10 = 0
Add 10 to each side.
5x - y = 10
Subtract 5x from each side.
-y = 10 - 5x
Multiply each side by (-1).
y = 5x - 10 -----(3)
Step 2 :
Substitute (5x - 10) for y into (1).
(2)-----> 3x + 5(5x - 10) - 6 = 0
3x + 25x - 50 - 6 = 0
28x - 56 = 0
Add 56 to each side.
28x = 56
Divide each side by 28.
x = 2
Step 3 :
Substitute 2 for x into (3).
(3)-----> y = 5(2) - 10
y = 10 - 10
y = 0
Therefore, the solution is
(x, y) = (2, 0)
Problem 5 :
Solve for x and y :
2x + 3y = 5
3x + 4y = 7
Solution :
2x + 3y = 5 -----(1)
3x + 4y = 7 -----(2)
Step 1 :
Multiply (1) by 3.
(1) ⋅ 3 -----> 6x + 9y = 15
Solve for 6x.
6x = 15 - 9y -----(3)
Step 2 :
Multiply (2) by 2.
(2) ⋅ 2 -----> 6x + 8y = 14
From (3), substitute (15 - 9y) for 6x.
(15 - 9y) + 8y = 14
Simplify.
15 - 9y + 8y = 14
15 - y = 14
Subtract 15 from each side.
-y = -1
Multiply each side by (-1).
y = 1
Step 3 :
Substitute 1 for y into (3).
(3)-----> 6x = 15 - 9(1)
6x = 15 - 9
6x = 6
Divide each side by 6.
x = 1
Therefore, the solution is
(x, y) = (1, 1)
After having gone through the stuff given above, we hope that the students would have understood how to solve system of equations by substitution.
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