The following steps will be useful to solve system of linear equations using method of substitution.

**Step 1 : **

In the given two equations, solve one of the equations either for x or y.

**Step 2 : **

Substitute the result of step 1 into other equation and solve for the second variable.

**Step 3 : **

Using the result of step 2 and step 1, solve for the first variable.

**Example 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)

**Example 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)

**Example 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)

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