Q 30 - Intermediate Algebra

Question

Solve the systems of equations by substitution.

$\left\{\begin{array}{l}2x+y=-4\\ 3x-2y=-6\end{array}\right.$

Step-by-Step Solution

Answer

The solution of system of linear equation is $(-2,0)$

Step 1. Given information

The system of equations is $\left\{\begin{array}{l}2x+y=-4\\ 3x-2y=-6\end{array}\right.$

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

$$\begin{gathered} 2x+y=-4 \\ y=-2x-4 \end{gathered}$$

Now,

$$\begin{gathered} 3x-2y=-6 \\ 3x-2(-2x-4)=-6 \\ 3x+4x+8=-6 \\ 7x=-14 \\ x=-2 \end{gathered}$$

Step 3. Substitute the value of x in any equation

$$\begin{gathered} 2x+y=-4 \\ 2(-2)+y=-4 \\ -4+y=-4 \\ y=0 \end{gathered}$$

Step 4. Required answer

The solution of system of linear equation is $(-2,0)$