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Abul · Answer 1 · 2023-05-06T18:43:47+0000

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

$\begin{gathered} (2x)/(3)\text{ - 2 = -x + 3} \\ \text{The common denominator for RHS is 3} \\ \frac{3(2x)/(3)\text{ - 3}(2)/(1)}{3}\text{ = -x + 3} \\ \frac{2x\text{ - 6}}{3}=\text{ -x + 3} \\ \text{Cross multiply} \\ 2x\text{ - 6 = 3(-x + 3)} \\ \text{Open the parenthesis} \\ 2x\text{ - 6 = -3x + 9} \\ 2x\text{ - 6 = -3x + 9} \\ \text{Collect the like terms} \\ 2x\text{ + 3x = 9 + 6} \\ 5x\text{ }=\text{ 15} \\ \text{Divide both sides by 5} \\ (5x)/(5)\text{ = }(15)/(5) \\ x\text{ = 3} \\ To\text{ find y, put the value of x in equation 2} \\ y\text{ = -x + 3} \\ y\text{ = -3 + 3} \\ y\text{ = 0} \end{gathered}$

Therefore, x = 3 and y = 0 --- (3, 0)

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