Q 50. - Intermediate Algebra

Question

In the following exercises, solve the systems of equations by elimination.

$$\begin{gathered} 3x-5y=-9 \\ 5x+2y=16 \end{gathered}$$

Step-by-Step Solution

Answer

The solution for system of linear equation is $\left(2,3\right)$.

Step 1. Given Information

System of linear equations:

$$\begin{gathered} 3x-5y=-9 .......\left(1\right) \\ 5x+2y=16 .......\left(2\right) \end{gathered}$$

Step 2. Calculation

Here both equations are in standard form. To get opposite coefficients of y multiply first equation with 2. 

$$\begin{gathered} 2\left(3x-5y\right)=2\left(-9\right) \\ 6x-10y=-18 ........\left(3\right) \end{gathered}$$

Also multiply second equation with 5.

$$\begin{gathered} 5\left(5x+2y\right)=5\left(16\right) \\ 25x+10y=80 ........\left(4\right) \end{gathered}$$

Solve for x:

From equations $\left(3\right)$and $\left(4\right)$:

$$\begin{gathered} 6x-10y=-18 \\ \underline{25x+10y=80} \\ 31x =62 \\ x=\frac{62}{31} \\ x=2 \end{gathered}$$

Solve for y:

Substitute $x=2$

in the equation  $3x-5y=-9$and solve for y.

$$\begin{gathered} 3x-5y=-9 \\ 3\left(2\right)-5y=-9 \\ 6-5y=-9 \\ -5y=-9-6 \\ -5y=-15 \\ y=\frac{-15}{-5} \\ y=3 \end{gathered}$$

The solution for system of linear equation is $\left(2,3\right)$.