Question

I am having so much trouble with my assignment. can you please help me with number 8 and 10.

Answer 1

We have to solve this system of equations by substitution.

8) First, we find the value of one of the variables in function of the other using one of the 2 equations (first equation, in this case). Then, we use the other equation and replace the variable we just cleared (x, int his case) and solve for the other variable (y).

Then, after calcualting y, we can use the first equation to calculate x.

$\begin{gathered} x+4y=0 \\ x=-4y \end{gathered}$$\begin{gathered} 3x+2y=20 \\ 3(-4y)+2y=20 \\ -12y+2y=20 \\ -10y=20 \\ y=\frac{20}{-10} \\ y=-2 \end{gathered}$$\begin{gathered} x=-4y=-4(-2) \\ x=8 \end{gathered}$

Answer: x=8, y=-2.

10)

$\begin{gathered} x-3y=-2 \\ x=3y-2 \end{gathered}$$\begin{gathered} 10x+8y=-20 \\ 10(3y-2)+8y=-20 \\ 30y-20+8y=-20 \\ 38y=-20+20 \\ 38y=0 \\ y=0 \end{gathered}$$x=3y-2=3\cdot0-2=0-2=-2$

Answer: x=-2, y=0