Question

How do you solve the following system: #5x-2y=-26, 6x + 7y = -9 #?

Answer 1

`x = -200/47` and `y = 111/47`

Explanation:

`5x - 2y = -26 color(white)(..)……(1)`
`6x + 7y = -9 color(white)(..) ……(2)`

Multiply equation `(1)` by `7` and equation `(2)` by `2`

`35x - 14y = -182`
`12x + 14y = -18`

Add both the equations

`35x - 14y + 12x + 14y = -182 - 18`

`47x = -200`

`color(blue)(x = -200/47`

Substitute `x = -200/47` in equation `(1)`

`5(-200/47) - 2y = -26`

`-1000/47 - 2y = -26`

`2y = -1000/47 + 26`

`2y = -1000/47 + (26 × 47/47)`

`2y = -1000/47 + 1222/47`

`2y = (-1000 + 1222)/47`

`2y = 222/47`

`y = 222/(2 × 47)`

`color(blue)(y = 111/47)`