Solving a system for x and y

[Kirsi_b]

Hi, I'm new to this and hope you can help me solve this problem. -4x-9y=-10 4y+15=x
I know I need to isolate the variables and solve from there, but I've been working on it so long it's just getting more confusing. So far, I keep getting x=-25 and y=-3.3, but I don't think I'm doing it correctly. Any help would be much appreciated. Thanks!

 

[soroban]

Hello, Kirsi_b!

\(\displaystyle \begin{array}{ccc}\text{-}4x-9y&=&\text{-}10 \\ 4y+15&=&x \end{array}\)

I know I need to isolate the variables and solve from there.
What method are you using?
So far, I keep getting x = -25 and y = -3.3, but I don't think I'm doing it correctly.
Don't you know how to check your answers?

Substitution Method

The second equation is already solved for \(\displaystyle x.\)

Substitute for \(\displaystyle x\) in the first equation:

. . \(\displaystyle \text{-}4(4y+15) - 9y \:=\:\text{-}10 \quad\Rightarrow\quad \text{-}16y - 60 - 9y \:=\:\text{-}10 \)

. . \(\displaystyle \text{-}25y \:=\:60 \quad\Rightarrow\quad \boxed{y \:=\:\text{-}2}\)

Substitute into the second equation:

. . \(\displaystyle 4(\text{-}2) + 15 \:=\: x \quad\Rightarrow\quad \boxed{x \:=\:7}\)