1 Answer

Ward Werbrouck · Answer 1 · 2023-02-28T12:31:59+0000

$\begin{cases}-2x-y=0\Rightarrow\text{ Equation 1} \\ x-y=0\Rightarrow\text{ Equation 2}\end{cases}$

Two points define a line. Then, we can take two values of x and replace them in each equation to get their respective y-coordinates.

Equation 1

$\begin{gathered} \text{If }x=2 \\ -2x-y=0 \\ -2(2)-y=0 \\ -4-y=0 \\ \text{ Add y from both sides of the equation} \\ -4-y+y=0+y \\ -4=y \\ \text{ Then, the line passes through the point (2,-4)} \end{gathered}$

$\begin{gathered} \text{If }x=-3 \\ -2x-y=0 \\ -2(-3)-y=0 \\ 6-y=0 \\ \text{ Add y from both sides of the equation} \\ 6-y+y=0+y \\ 6=y \\ \text{ Then, the line passes through the point (-3,6)} \end{gathered}$

Now we can graph and connect the points to obtain the graph of this line:

Equation 2

$\begin{gathered} \text{If }x=0 \\ x-y=3 \\ 0-y=3 \\ -y=3 \\ \text{ Multiply by -1 from both sides of the equation} \\ -y\cdot-1=3\cdot-1 \\ y=-3 \\ \text{ Then, the line passes through the point (0,-3)} \end{gathered}$
$\begin{gathered} \text{ If }x=1 \\ x-y=3 \\ 1-y=3 \\ \text{ Subtract 1 from both sides of the equation} \\ -y=2 \\ \text{ Multiply by -1 from both sides of the equation} \\ -y\cdot-1=2\cdot-1 \\ y=-2 \\ \text{ Then, the line passes through the point (1,-2)} \end{gathered}$

Now we can graph and connect the points to obtain the graph of this line:

Finally, the solution of the system is the point at which the lines intersect:

Therefore, the solution of the system is