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*(-4x)+2*(-6)=-4 \\ 2x-8x-12=-4 \\ -6x-12=-4 \\ -6x-12+12=-4+12 \\ -6x=-4+12 \\ -6x=8 \\ (-6x)/(-6)=(8)/(-6) \\ x*(-6)/(-6)=(8)/(-6) \\ x=-(8)/(6)=-(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*(x)-6 \\ y=-4*(-(4)/(3))-6 \\ y=(-4*-4)/(3)-6 \\ y=(4*4)/(3)-6 \\ y=(16)/(3)-6 \\ y=(16)/(3)-6*(3)/(3) \\ y=(16)/(3)-(6*3)/(3) \\ y=(16)/(3)-(18)/(3) \\ y=(16-18)/(3)=(-2)/(3)=-(2)/(3) \end{gathered}`

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