Question

Solve the system using substitution. Check your answer.
9x - 8y = 1
8y = x-1

Answer 1

all work is shown and pictured

Answer 2

x = 0 and y =-
`(1)/(8)`

The solution to the system of the equation is (0, -
`(1)/(8)` )

Explanation:

9x - 8y = 1 ----------------------------------(1)

8y = x-1----------------------------------------(2)

From equation (2)

8y = x -1

we will make x the subject of the formula, we will do this by adding 1 to both-side of the equation

8y + 1 = x -1 + 1

8y + 1 = x

x = 8y + 1 ----------------------------------------(3)

Substitute equation (3) in equation (1)

9x - 8y = 1

9(8y + 1) - 8y = 1

Open the bracket by multiplying 9 with all the values in the bracket

72y + 9 - 8y = 1

Rearrange the equation

72y - 8y + 9 = 1

64y + 9 = 1

subtract 9 from both-side of the equation

64y + 9 -9 = 1 - 9

64y = -8

Divide both-side of the equation by 64

64y/64 = -8/64

y= -
`(1)/(8)`

Substitute y=-
`(1)/(8)` in equation (3)

x = 8y + 1

x = 8(-
`(1)/(8)` ) + 1

x = -1 + 1

x = 0

Therefore x = 0 and y = -
`(1)/(8)`

The solution to the system of the equation is (0, -
`(1)/(8)` )