Question

X 5x – 3y = -20 4x + 5y = -2

Answer 1

Answer:

$\huge\boxed{\left\{\begin{array}{ccc}x=-\dfrac{106}{37}\\y=\dfrac{70}{37}\end{array}\right}$

Step-by-step explanation:

$\left\{\begin{array}{ccc}5x-3y=-20&\text{multiply both sides by 5}\\4x+5y=-2&\text{multiply both sides by 3}\end{array}\right\\\underline{+\left\{\begin{array}{ccc}25x-15y=-100\\12x+15y=-6\end{array}\right}\qquad\text{add both sides of the equations}\\.\qquad37x=-106\qquad\text{divide both sides by 37}\\.\qquad\boxed{x=-\dfrac{106}{37}}$

$\text{Substitute it to the first equation}\\\\5\left(-\dfrac{106}{37}\right)-3y=-20\\\\-\dfrac{530}{37}-3y=-20\qquad\text{multiply both sides by (-37)}\\\\(-37\!\!\!\!\!\diagup)\left(-\dfrac{530}{37\!\!\!\!\!\diagup}\right)-(-37)(3y)=(-37)(-20)\\\\530+111y=740\qquad\text{subtract 530 from both sides}\\\\111y=210\qquad\text{divide both sides by 111}\\\\y=\dfrac{210}{111}\\\\y=\dfrac{210:3}{111:3}\\\\\boxed{y=\dfrac{70}{37}}$

Answer 2

Answer:

x=-106/37

y=70/37

Step-by-step explanation:

I chose to set up the problem as a matrix to solve here.

(Another way to do this would be to isolate one variable in one of the equations, substitute it into the other equation, solve for that, and then plug it back in to get the final variable.)

My work is in the attachment. Lmk if you have any questions.