Question

Use substitution to solve each system of equation.

$\begin{array}{c}\mathbf{x}\mathbf{=}\mathbf{-}\mathbf{4}\mathbf{y}\mathbf{-}\mathbf{3}\\ \mathbf{3}\mathbf{x}\mathbf{-}\mathbf{2}\mathbf{y}\mathbf{=}\mathbf{5}\end{array}$

Short answer

The solution of the given system of equations is $\mathbf{(}\mathbf{1}\mathbf{,}\mathbf{-}\mathbf{1}\mathbf{)}$.

Step-by-step solution

Step 1. Write the given system of equations.

The given system of equations is:

$\begin{array}{l}x=-4y-3...\left(1\right)\\ 3x-2y=5....\left(2\right)\end{array}$

Step 2. Solve the given system of equations.

Substitute the value of$x$from the equation (1) in the equation (2).

$\begin{array}{c}3x-2y=5\\ 3(-4y-3)-2y=5\\ -12y-9-2y=5\\ -14y=5+9\\ -14y=14\\ y=\frac{14}{-14}\\ y=-1\end{array}$

The value of$y$is$-1$.

Substitute$-1$for$y$in the equation (1) to find the value of$x$.

$\begin{array}{c}x=-4y-3\\ =-4(-1)-3\\ =4-3\\ =1\end{array}$

The value$x$of is 1.

Therefore, the solution of the given system of equations is$(1,-1)$.