Question

How do you solve the following system: #5x - 7y = 12 , x + 8y = 15 #?

Answer 1

The solution for the system of equations is:
`color(green)(x=201/47 , y = 63/47`

Explanation:

`color(blue)(5x) - 7y =12`.............equation `(1)`

`x + 8y = 15`, multiplying by `5`
`color(blue)(5x) + 40y = 75` ..........equation `(2)`

Solving by elimination:

Subtracting equation `2` from equation `1:`

`cancelcolor(blue)(5x) - 7y =12`
`-cancelcolor(blue)(5x) - 40y = -75`

`-47 y = -63`

`y = -63 / (47 )`

`color(green)(y = 63/47`

Finding `x` from equation `2`
`x + 8y = 15`

`x = 15 - 8y`

`x = 15 - 8 * (63/47)`

`x = 15 - 504/47`

`x = 705 /47 - 504/47`

`color(green)(x = 201/47`