Question

Solve the system of equation by graphing.Y=-1/2x-1Y=1/4x-4Please graph and solve the equation

Answer 1

$\begin{gathered} x=4 \\ y=-3 \end{gathered}$

Explanation

Step 1

to solve this we need to graph both lines

a) find two coordinates of line 1

$y=-\frac{1}{2}x-1$

$\begin{gathered} whenx=0 \\ y=-\frac{1}{2}x-1 \\ y=-\frac{1}{2}\cdot0-1 \\ y=0-1 \\ y=-1 \\ \text{then, (0,-1)}\rightarrow P1 \end{gathered}$

now, when x=4

$\begin{gathered} y=-\frac{1}{2}x-1 \\ y=-\frac{1}{2}(4)-1 \\ y=-2-1 \\ y=-3 \\ \text{then, (4,-3)}\rightarrow P2 \end{gathered}$

now, using P1 and P2 draw the line

Step 2

Now, the line 2

$y=\frac{1}{4}x-4$

when x=0(you can take the value you want)

$\begin{gathered} y=\frac{1}{4}x-4 \\ y=\frac{1}{4}(0)-4 \\ y=0-4 \\ y=-4 \\ \text{then,}(0,-4)\rightarrow P3 \end{gathered}$

when x=4

$\begin{gathered} y=\frac{1}{4}x-4 \\ y=\frac{1}{4}(4)-4 \\ y=1-4 \\ y=-3 \\ \text{then,}(4,-3)\rightarrow P4 \end{gathered}$

draw the line 2 using points P3 and P4.

Step 3

finally, the solution is the point where the lines intersect each other,

graph:

Hence, the answer is

$\begin{gathered} (4,-3) \\ x=4 \\ y=-3 \end{gathered}$

I hope this helps you