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:

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