# SOLVING SYSTEM OF EQUATIONS BY SUBSTITUTION WORKSHEET

Problem 1 :

Solve for x and y :

x + y = 5

2x + 3y = 5

Problem 2 :

Solve for x and y :

2x + 5y = 12

4x - y = 2

Problem 3 :

Solve for x and y :

x + y - 4 = 0

2x - 3y - 18 = 0

Problem 4 :

Solve for x and y :

3x + 5y = -2

2x - y = 3

Problem 5 :

If there is a total of 9 bicycles and unicycles and there are 13 wheels in total, find the number of bicycles and unicycles.

x + y = 5 ----(1)

2x + 3y = 5 ----(2)

Step 1 :

Solve (1) for y.

x + y = 5

Subtract x from each side.

y = 5 - x ----(3)

Step 2 :

Substitute (5 - x) for y into (2).

2x + 3(5 - x) = 5

2x + 15 - 3x = 5

15 - x = 5

Subtract 15 from each side.

-x = -10

Multiply each side by (-1).

x = 10

Step 3 :

Substitute 10 for x into (3).

y = 5 - 10

y = -5

Therefore, the solution is

(x, y) = (10, -5)

2x + 5y  =  12 -----(1)

4x - y  =  2 -----(2)

Step 1 :

Solve (2) for y.

4x - y = 2

Subtract 4x from each side.

-y = 2 - 4x

Multiply each side by (-1).

y = 4x - 2 -----(3)

Step 2 :

Substitute (4x - 2) for y into (1).

2x + 5(4x - 2) = 12

2x + 20x - 10 = 12

22x - 10 = 12

22x = 22

Divide each side by 22.

x = 1

Step 3 :

Substitute 1 for x into (3).

y = 4(1) - 2

y = 4 - 2

y = 2

Therefore, the solution is

(x, y) = (1, 2)

x + y - 4 = 0 ----(1)

2x - 3y - 18 = 0 ----(2)

Step 1 :

Solve (1) for x.

x + y - 4 = 0

x + y = 4

Subtract y from each side.

x = 4 - y ----(3)

Step 2 :

Substitute (4 - y) for x into (2).

2(4 - y) - 3y - 18 = 0

8 - 2y - 3y - 18 = 0

-5y - 10 = 0

-5y = 10

Divide each side by -5.

y = -2

Step 3 :

Substitute (-2) for y into (3).

x = 4 - (-2)

x = 4 + 2

x = 6

Therefore, the solution is

(x, y) = (6, -2)

3x + 5y = -2 ----(1)

2x - y = 3 ----(2)

Step 1 :

Solve (2) for y.

2x - y = 3

Subtract 2x from each side.

-y = 3 - 2x

Multiply each side by (-1).

y = 2x - 3 ----(3)

Step 2 :

Substitute (2x - 3) for x into (1).

(2)----> 3x + 5(2x - 3) = -2

3x + 10x - 15 = -2

13x - 15 = -2

13x = 13

Divide each side by 13.

x = 1

Step 3 :

Substitute 1 for x into (3).

y = 2(1) - 3

y = 2 - 3

y = -1

Therefore, the solution is

(x, y) = (1, -1)

Let x be the number of bicycles and y be the number of unicycles.

Given : There is a total of 9 bicycles and unicycles.

x + y = 9 ----(1)

Given : There are 13 wheels in total.

2x + y = 13 ----(2)

Step 1 :

Solve (1) for x.

x + y = 9

Subtract y from each side.

x = 9 - y ----(3)

Step 2 :

Substitute (9 - y) for x into (2).

2(9 - y) + y = 13

18 - 2y + y = 13

18 - y = 13

Subtract 13 from each side.

-y = -5

Multiply each side by (-1).

y = 5

Step 3 :

Substitute 5 for y into (3).

x = 9 - 5

x = 4

The solution is

(x, y) = (5, 4)

So, there are 5 bicycles and 4 unicycles.

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