Answer: x = 3 and y = 0
Given that
y = 2/3x - 2 ------------- equation 1
y = -x + 3 ---------------- equation 2
These system of linear equation can be solve simultaneously
equate equation 1 and 2 together
[tex]\begin{gathered} \frac{2x}{3}\text{ - 2 = -x + 3} \\ \text{The common denominator for RHS is 3} \\ \frac{3\frac{2x}{3}\text{ - 3}\frac{2}{1}}{3}\text{ = -x + 3} \\ \frac{2x\text{ - 6}}{3}=\text{ -x + 3} \\ \text{Cross multiply} \\ 2x\text{ - 6 = 3(-x + 3)} \\ \text{Open the parenthesis} \\ 2x\text{ - 6 = -3x + 9} \\ 2x\text{ - 6 = -3x + 9} \\ \text{Collect the like terms} \\ 2x\text{ + 3x = 9 + 6} \\ 5x\text{ }=\text{ 15} \\ \text{Divide both sides by 5} \\ \frac{5x}{5}\text{ = }\frac{15}{5} \\ x\text{ = 3} \\ To\text{ find y, put the value of x in equation 2} \\ y\text{ = -x + 3} \\ y\text{ = -3 + 3} \\ y\text{ = 0} \end{gathered}[/tex]Therefore, x = 3 and y = 0 --- (3, 0)
