Question

solve this system of equations by graphing. first graph the equations, and then type the solution.
y = -\frac{2}{3}x + 2
y = \frac{1}{2}x - 5
click to select points on the graph.
the solution is ( , ).
submit

Explanation:

Step1: Set the two equations equal

Since at the solution point, the \(y -\)values of the two equations are equal, we set \(-\frac{2}{3}x + 2=\frac{1}{2}x-5\).

Step2: Get a common - denominator

Multiply through by 6 to clear the fractions. We get \(6\times(-\frac{2}{3}x)+6\times2 = 6\times\frac{1}{2}x-6\times5\), which simplifies to \(- 4x + 12=3x-30\).

Step3: Isolate the \(x\) - terms

Add \(4x\) to both sides: \(12 = 3x+4x-30\), or \(12 = 7x-30\).

Step4: Solve for \(x\)

Add 30 to both sides: \(12 + 30=7x\), so \(42 = 7x\). Then divide both sides by 7, and we find \(x = 6\).

Step5: Solve for \(y\)

Substitute \(x = 6\) into the second equation \(y=\frac{1}{2}x - 5\). Then \(y=\frac{1}{2}\times6-5=3 - 5=-2\).

Answer:

\((6,-2)\)