Question

systems if equations-4x-y=62x+2y= -4

Answer 1

We can solve this system of linear equations by following these steps:

1. solve for y from the first equation:

$\begin{gathered} -4x-y=6 \\ -4x-y+y=6+y \\ -4x=6+y \\ -4x-6=6-6+y \\ y=-4x-6 \end{gathered}$

2. replace the above expression into the second equation and find the value of x:

$\begin{gathered} 2x+2y=-4 \\ 2x+2(-4x-6)=-4 \\ 2x+2\times(-4x)+2\times(-6)=-4 \\ 2x-8x-12=-4 \\ -6x-12=-4 \\ -6x-12+12=-4+12 \\ -6x=-4+12 \\ -6x=8 \\ \frac{-6x}{-6}=\frac{8}{-6} \\ x\times\frac{-6}{-6}=\frac{8}{-6} \\ x=-\frac{8}{6}=-\frac{4}{3} \end{gathered}$

3. replace the value of x into the expression y= -4x-6 and calculate the value of y, like this:

$\begin{gathered} y=-4\times(x)-6 \\ y=-4\times(-\frac{4}{3})-6 \\ y=\frac{-4\times-4}{3}-6 \\ y=\frac{4\times4}{3}-6 \\ y=\frac{16}{3}-6 \\ y=\frac{16}{3}-6\times\frac{3}{3} \\ y=\frac{16}{3}-\frac{6\times3}{3} \\ y=\frac{16}{3}-\frac{18}{3} \\ y=\frac{16-18}{3}=\frac{-2}{3}=-\frac{2}{3} \end{gathered}$

Solution: x equals -4/3 and y equals -2/3