Question

In Problems 1–4, solve each system of equations using the method of substitution or the method of elimination. If the system has no solution, say that it is inconsistent.

$\left\{\begin{array}{l}-2x+y=-7\\ 4x+3y=9\end{array}\right.$

Short answer

The solution of the system of equations $\left\{\begin{array}{l}-2x+y=-7\\ 4x+3y=9\end{array}\right.$ is $(3,-1)$

Step-by-step solution

Step 1. Given

The system of equations:

$\left\{\begin{array}{l}-2x+y=-7\\ 4x+3y=9\end{array}\right.$

Step 2. Solve the equation

Multiply the first equation by $2$,

$-4x+2y=-14$

Add the above equation with second equation, we get,

$$\begin{gathered} 5y=-5 \\ y=-1 \end{gathered}$$

Step 3. Find x

Substitute $y=-1$in the second equation,

$$\begin{gathered} 4x+3y=9 \\ 4x+3(-1)=9 \\ 4x=12 \\ x=3 \end{gathered}$$

Step 4. Check the solution

Substitute $x=3;y=-1$in the first equation,

$$\begin{gathered} -2x+y=-7 \\ -2\left(3\right)+(-1)=-7 \\ -7=-7 \end{gathered}$$

Hence the solution is checked.