Question

O solve this system of equations by addition, what could you multiply each equation by to cancel out the x-variable? A: 5x - 2y = 10 B: 4x + 3y = 7

Answer 1

Multiply `5x-2y=10` by `4`.
Multiply `4x+3y=7` by `5`.

Explanation:

In order to cancel out the `x` variable, the coefficient of `x` in both equations must be equal. Thus, find the L.C.M. (lowest common multiple) of `4` and `5`, which is `20`.

For `5x-2y=10`, in order to make the coefficient of `5x` be `20`, the whole equation must be multiplied by `4`.

`4(5x-2y=10)`

`color(darkorange)("Equation"color(white)(i)1)`: `20x-8y=40`

Similarly, for `4x+3y=7`, in order to make the coefficient of `4x` be `20`, the whole equation must be multiplied by `5`.

`5(4x+3y=7)`

`color(darkorange)("Equation"color(white)(i)2`: `20x+15y=35`

Since elimination works by subtracting one equation from the other, if you try subtracting equation `2` from equation `1`, the terms with `x` will become `color(blue)("zero")`.

`color(white)(Xx)20x-8y=40`
`(-(20x+15y=35))/(color(blue)(0x)-23y=5)`