Question

Solve the following systems using the substitution method.

Answer 1

Answer:

Step-by-step explanation:

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Answer 2

Step-by-step explanation:

1).

2x + 8y = 12 ......... Equation 1

x - 2y = 0 .............. Equation 2

Make x the subject in equation 2 and substitute it into equation 1

That's

x = 2y

We have

2(2y) + 8y = 12

4y + 8y = 12

12y = 12

Divide both sides by 12

y = 1

Substitute y = 1 into x = 2y

That's

x = 2(1)

x = 2

The answers are

x = 2 , y = 1

2.)

x + y = 7......... Equation 1

2x + y = 5 ......... Equation 2

Make y the subject in equation 1 and substitute it into equation 2

We have

y = x - 7

2x + x - 7 = 5

3x = 7 + 5

3x = 12

Divide both sides by 3

x = 4

Substitute x = 4 into y = x - 7

y = 4 - 7

y = - 3

We have the answers as

x = 4 , y = - 3

3).

y = -1/2 + 1 ......... Equation 1

2x + 3y = 6 ........ Equation 2

From equation 1

y = 1/2

Substitute y = 1/2 into Equation 2

So we have

2x + 3(1/2) = 6

2x + 3/2 = 6

2x = 6 - 3/2

2x = 9/2

Divide both sides by 2

x = 9/4

The answers are

x = 9/4 , y = 1/2

4).

2x - 1/3y = - 9.......... Equation 1

-3x + y = 15 ........... Equation 2

Make y the subject in equation 2 and substitute it into equation 1

That's

y = 15 + 3x

2x - 1/3( 15 + 3x) = - 9

2x - 5 - x = - 9

x = - 9 + 5

x = - 4

Substitute x = - 4 into y = 15 + 3x

That's

y = 15 + 3(-4)

y = 15 - 12

y = 3

The answers are

x = - 4 , y = 3

Hope this helps you