graph the 2 lines, find the solution to the system\n$y=-x + 4$\n$y=\frac{2}{5}x-3$

Explanation:

Step1: Set the two equations equal

Since $y=-x + 4$ and $y=\frac{2}{5}x-3$, we set $-x + 4=\frac{2}{5}x-3$.

Step2: Get rid of the fraction

Multiply through by 5 to clear the fraction: $5(-x + 4)=5(\frac{2}{5}x-3)$. This gives $-5x+20 = 2x-15$.

Step3: Isolate the x - terms

Add $5x$ to both sides: $20=2x + 5x-15$, so $20 = 7x-15$.

Step4: Solve for x

Add 15 to both sides: $20 + 15=7x$, then $35 = 7x$. Divide both sides by 7, we get $x = 5$.

Step5: Solve for y

Substitute $x = 5$ into the first equation $y=-x + 4$. So $y=-5 + 4=-1$.

Answer:

The solution to the system is $(5,-1)$.