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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