Question

The solution to the system is (3, 4):
3x - 2y = 1
4y = 7+3x

Answer 1

See the work below.

Explanation:

If 3x-2y=1, then

`x=((1)/(3))1+2y`

Substitute for x in 4y=7+3x.

`4y=7+3((1)/(3))(1+2y)\\4y=7+(1+2y)\\4y=7+1+2y\\4y=8+2y\\4y-2y=8+2y-2y\\2y=8\\y=4`

Substitute y=4 in 3x-2y=1

`3x-2(4)=1\\3x-8=1\\3x-8+8=1+8\\3x=9\\(3x)/(3)=(9)/(3)\\x=3`

This work proves the given values are correct.

Answer 2

(3,4)

Explanation:

3x - 2y = 1

-3x + 4y = 7

3x - 3x = 0

-2y + 4y = 2y

1+7 = 8

2y = 8

2/2 y = 8/2

y = 4

3x -2(4) = 1

3x - 8 = 1

3x = 8 + 1

3x = 9

3/3 x = 9/3

x = 3