Question

How do you solve the system of equations `3x+2y = 13` and `x+5y = 13` by elimination?

Answer 1

`(x,y)=(3,2)`

Explanation:

`color(blue)(3x+2y=13`

`color(blue)(x+5y=13)`

You can see clearly that,we can eliminate `3x` in the first equation by `x` in the second equation if we multiply it with `-3` to get `-3x`

`rarr-3(x+5y=13)`

`rarr-3x-15y=-39`

Add both the equations

`rarr(3x+2y=13)+(-3x-15y=-39)`

`rarr-13y=-26`

`color(green)(rArry=(-26)/-13=26/13=2`

Substitute the value of `y` to the second equation

`rarrx+5(2)=13`

`rarrx+10=13`

`color(green)(rArrx=13-10=3`

But before concluding it Check your answer

`1)`Check `color(blue)((3x+2y=13)`

`rarr3(3)+2(2)=13`

`rarr9+4=13`

`color(green)(|->13=13`

`2)`Check `color(blue)((x+5y=13)`

`rarr3+5(2)=13`

`rarr3+10=13`

`color(green)(|->13=13`

`:.color(indigo)(ul bar |x,y=3,2|`