Question

solve the following system equation7x+9y=95x+3y=-21x=y=

Answer 1

$\mleft\{\begin{aligned}7x+9y=9 \\ 5x+3y=-21\end{aligned}\mright.$

We can solve this system by elimination. So we are goinf to multiply the first equation by 1 and the second one by -3. Just to have the same coefficient in the variable y:

$\mleft\{\begin{aligned}7x+9y=9 \\ -15x-9y=63\end{aligned}\mright.$

adding the equation we have that

$\begin{gathered} -8x+0y=72 \\ x=-\frac{72}{8}=-9 \end{gathered}$

if x=-9, we have that

$\begin{gathered} 7\cdot-9+9\cdot y=9 \\ -63+9y=9 \\ 9y=72 \\ y=\frac{72}{9}=8 \end{gathered}$

so x=-9 and y=8