Question

Solve the system of linear equations by substitution. y = -2x - 9 Equation 6x - 5y = -19 Equation 2

Answer 1

Solving by substitution method.

We have 2 equations:

$y=-2x-9$

and

$6x-5y=-19$

If we substitute the first equation into the second one, we get

$6x-5(-2x-9)=-19$

which gives

$\begin{gathered} 6x-5(-2x)-5(-9)=-19 \\ 6x+10x+45=-19 \\ 6x+45=-19 \\ 6x=-19-45 \\ 6x=-64 \\ x=-\frac{64}{6} \\ x=-10.666 \end{gathered}$

Now, we can substitute this result into the first equation, then we get

$y=-2(-10.66)-9$

then, we have

$\begin{gathered} y=21.33-9 \\ y=12.33 \end{gathered}$

Therefore, the solution of the system is

$\begin{gathered} x=-10.66 \\ \text{and} \\ y=12.33 \end{gathered}$