Q 32 - Intermediate Algebra

Question

Solve the systems of equations by substitution. 

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

Step-by-Step Solution

Answer

The solution of system of linear equation is $(7,6)$

Step 1. Given information

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

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

$$\begin{gathered} x-2y=-5 \\ 2y=x+5 \\ y=\frac{x}{2}+\frac{5}{2} \end{gathered}$$

Now,

$$\begin{gathered} 2x-3y=-4 \\ 2x-3\left(\frac{x}{2}+\frac{5}{2}\right)=-4 \\ 2x-\frac{3x}{2}-\frac{15}{2}=-4 \\ \frac{x}{2}=\frac{7}{2} \\ x=7 \end{gathered}$$

Step 3. Substitute the value of x in any equation

$$\begin{gathered} x-2y=-5 \\ 7-2y=-5 \\ -2y=-12 \\ y=6 \end{gathered}$$

Step 4. Required answer

The solution of system of linear equation is $(7,6)$