What is the first step in solving this system of equations by elimination? 5a + 3b = - 9 2a - 5b = - 16

Multiply one of the equations so that both equations share a common complementary coefficient.

In order to solve using the elimination method, you need to have a matching coefficient that will cancel out a variable when you add the equations together. For the 2 equations given, you have a huge number of choices. I'll just mention a few of them.

You can multiply the 1st equation by - 2/5 to allow cancelling the a term.

You can multiply the 1st equation by 5/3 to allow cancelling the b term.

You can multiply the 2nd equation by - 2.5 to allow cancelling the a term. You can multiply the 2nd equation by 3/5 to allow cancelling the b term.

You can even multiply both equations.

For instance, multiply the 1st equation by 5 and the second by 3. And in fact, let's do that. 5a + 3b = â€"9 2a â€" 5b = â€"16 5 * (5a + 3b = - 9) = 25a + 15b = - 45

3 * (2a - 5b = - 16) = 6a - 15b = - 48

Then add the equations 25a + 15b = - 45

6a - 15b = - 48

=

31a = - 93

a = - 3

And then plug in the discovered value of a into one of the original equations and solve for b.