The solution (x, y) = (3, -2)
Explanation:
y = -x + 1
y = 2/3x - 4
Using the equal method:
we would equate both equation together. This because they are both equal to y
y = y
-x + 1 = 2/3x - 4
[tex]\begin{gathered} -x+1=\frac{2}{3}x-4 \\ \text{add x to both sides:} \\ -x\text{ + x }+1=\frac{2}{3}x+x-4 \\ \end{gathered}[/tex][tex]\begin{gathered} 0+1=\frac{2x+3(x)}{3}-4 \\ 1\text{ = }\frac{5x}{3}-4 \\ \text{add 4 to both sides:} \\ 1+4\text{ = }\frac{5x}{3}-4+4 \end{gathered}[/tex][tex]\begin{gathered} 5\text{ = }\frac{5x}{3}+0 \\ \frac{5}{1}\text{ = }\frac{5x}{3} \\ cross\text{ multiply}\colon \\ 5(3)\text{ = 5x} \\ 15\text{ = 5x} \\ \text{divide both sides by 5:} \\ \frac{15}{5\text{ }}=\text{ }\frac{\text{5x}}{5} \\ 3\text{ = x} \end{gathered}[/tex]
We replace x in any of the equation with 3 to get y:
using the first equation: y = -x + 1
y = -3 + 1
y = -2
The solution or the point of intersection (x, y) = (3, -2)
