Question

solve this system of equations by graphing. first graph the equations, and then type the solution.
y = 1/2x - 6
y = -x
click to select points on the graph.
the solution is ( , ).

Explanation:

Step1: Set the two equations equal.

$\frac{1}{2}x - 6=-x$

Step2: Add $x$ to both sides.

$\frac{1}{2}x+x - 6=-x+x$, which simplifies to $\frac{1}{2}x+\frac{2}{2}x - 6 = 0$, then $\frac{3}{2}x-6 = 0$.

Step3: Add 6 to both sides.

$\frac{3}{2}x-6 + 6=0 + 6$, so $\frac{3}{2}x=6$.

Step4: Solve for $x$.

Multiply both sides by $\frac{2}{3}$, we get $x = 6\times\frac{2}{3}=4$.

Step5: Find $y$ - value.

Substitute $x = 4$ into $y=-x$, then $y=-4$.

Answer:

$(4,-4)$