Question

[6.01] What is the first step to solving the system by eliminatingthe y variable first?4x − 5y = 43x + 2y = −20

Answer 1

ANSWER:

x = -4 and y = -4

STEP-BY-STEP EXPLANATION:

We have the following system of equations:

$\begin{gathered} 4x-5y=4 \\ 3x+2y=-20 \end{gathered}$

We solve by elimination:

To eliminate the variable y first, we multiply the first equation by 2 and the second equation by 5, just like this:

$\begin{gathered} 2\cdot(4x-5y)=2\cdot4\rightarrow8x-10y=8 \\ 5\cdot(3x+2y)=5\cdot-20\rightarrow15x+10y=-100 \\ \text{ now, we add the equations:} \\ 8x-10y+15x+10y=8-100 \\ 23x=-92 \\ x=-\frac{92}{23} \\ x=-4 \\ \text{solve for y:} \\ -4\cdot-4-5y=4 \\ -5y=4+16 \\ y=\frac{20}{-5} \\ y=-4 \end{gathered}$