SUBSTITUTION METHOD WORKSHEET
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
Detailed Answer Key
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)
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