Question

Use elimination method to solve 5x+y=-10 7x-3y=-36

Answer 1

$5x+y=-10\\ \\ 7x-3y=-36$

Let's multiply the first equation by 3. (As you can see y's coefficient in the first one is 1 and in the second one is -3 , we will multiply the first equation by 3 so when we add the equations their sum will be 0)

$3\cdot (5x+y)=3\cdot -10\\ \\ 15x+3y=-30$

Now let's add this new equation and our second equation.

$7x-3y=-36\\ \\ 15x+3y=-30\\ \\ (15x+3y)+(7x-3y)=(-30)+(-36)\\ \\ 15x+7x+3y-3y=-30-36\\ \\ 22x=-66\\ \\ x=\frac { -66 }{ 22 } \\ \\ x=-3$

We found x=-3

Now let's plug x's value in one of the equations to find y's value.

$x=-3\\ \\ 5x+y=-10\\ \\ 5\cdot -3+y=-10\\ \\ -15+y=-10\\ \\ y=-10+15\\ \\ y=5$

So we found y=5

Solution ;

(-3, 5)