Question

intro to sy
graph each system of equations to fin
to both equations. be sure to show a
. ( y = -x + 6 ) and ( y = \frac{2}{3}x - 9 )

olution:
( y = 3x - 4 ) and ( y = -\frac{1}{2}x + 10 )

Explanation:

Step1: Solve the system algebraically (to find intersection)

Set \(-x + 6=\frac{2}{3}x - 9\). Add \(x\) to both sides: \(6=\frac{2}{3}x+x - 9\). Combine like terms: \(6=\frac{5}{3}x - 9\). Add 9: \(15=\frac{5}{3}x\). Multiply by \(\frac{3}{5}\): \(x = 9\). Substitute \(x = 9\) into \(y=-x + 6\): \(y=-9 + 6=-3\).

Step2: Verify in both equations

For \(y=-x + 6\): \(y=-9 + 6=-3\) (correct). For \(y=\frac{2}{3}x - 9\): \(y=\frac{2}{3}(9)-9 = 6 - 9=-3\) (correct).

Answer:

The solution is \((9, -3)\)