Question

solve the following system of equations graphically on the set of axes below. y = 1/5x + 6 4x + 5y = 5 plot two lines by clicking the graph. click a line to delete it.

Explanation:

Step1: Rewrite the second - equation in slope - intercept form

Starting with \(4x + 5y=5\), solve for \(y\). Subtract \(4x\) from both sides: \(5y=-4x + 5\). Then divide by \(5\): \(y=-\frac{4}{5}x + 1\).

Step2: Find the intersection point by setting the two equations equal

Set \(\frac{1}{5}x+6=-\frac{4}{5}x + 1\). Add \(\frac{4}{5}x\) to both sides: \(\frac{1}{5}x+\frac{4}{5}x+6=-\frac{4}{5}x+\frac{4}{5}x + 1\), which simplifies to \(x + 6=1\). Subtract \(6\) from both sides: \(x=1 - 6=-5\).

Step3: Find the \(y\) - value

Substitute \(x = - 5\) into \(y=\frac{1}{5}x+6\). Then \(y=\frac{1}{5}\times(-5)+6=-1 + 6=5\).

Answer:

The solution of the system is \(x=-5,y = 5\)