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}`

Step-by-step explanation

Step 1

to solve this we need to graph both lines

a) find two coordinates of line 1

`y=-(1)/(2)x-1`

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

now, when x=4

`\begin{gathered} y=-(1)/(2)x-1 \\ y=-(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=(1)/(4)x-4`

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

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

when x=4

`\begin{gathered} y=(1)/(4)x-4 \\ y=(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