Question

Solve for x and y:

3x – 5y = 4, 2y + 7 = 9x

Answer 1

Given: 3x – 5y = 4, 2y + 7 = 9x

Step-wise calculation:

1. From 2y + 7 = 9x

Isolate y: 2y = 9x – 7 

⇒ `y = (9x - 7)/2`

2. Substitute y into 3x – 5y = 4:

`3x - 5 [(9x - 7)/2] = 4` 

Multiply both sides by 2:

6x – 5(9x – 7) = 8

6x – 45x + 35 = 8

–39x + 35 = 8 

–39x = 8 – 35

–39x = –27 

`x = (-27)/(-39)` 

= `27/39`

= `9/13`

3. Find y using `y = (9x - 7)/2`: 

`y = (9 xx (9/13) - 7)/2` 

= `(81/13 - 91/13)/2`

= `((-10)/13)/2`

= `(-10)/26`

= `(-5)/13`

4. (Quick check) `3x - 5y = 3 xx (9/13) - 5 xx ((-5)/13)`

= `(27 + 25)/13` 

= `52/13`

= 4

And `2y + 7 = 2 xx ((-5)/13) + 7`

= `(-10)/13 + 91/13`

= `81/13`

= `9 xx (9/13)`

`x = 9/13, y = (-5)/13`