Question

Solve the systems of equations by substitution.

$\left\{\begin{array}{l}x-3y=-9\\ 2x+5y=4\end{array}\right.$

Short answer

The solution of system of linear equation is $(-3,2)$

Step-by-step solution

Step 1. Given information

The system of equations is$\left\{\begin{array}{l}x-3y=-9\\ 2x+5y=4\end{array}\right.$

Step 2. Substitute the value of x from one equation into other equation 

$$\begin{gathered} x-3y=-9 \\ x=3y-9 \end{gathered}$$

Now,

$$\begin{gathered} 2x+5y=4 \\ 2(3y-9)+5y=4 \\ 6y-18+5y=4 \\ 11y=22 \\ y=2 \end{gathered}$$

Step 3. Substitute the value of y in any equation 

$$\begin{gathered} x-3y=-9 \\ x-3\left(2\right)=-9 \\ x-6=-9 \\ x=-3 \end{gathered}$$

Step 4. Required answer

The solution of system of linear equation is$(-3,2)$