Question

Solve the system of equations.y=x−5y=x2−2x−9 Enter your answers in the boxes.(, ) or (, )

Answer 1

(4, -1) or (-1, -6)

Step-by-step explanation

Given that;

`\begin{gathered} \text{ y = x - 5 ------ equation 1} \\ \text{ y = x}^2\text{ - 2x - 9 ---- equation 2} \end{gathered}`

Follow the steps below to find the value of x and y

Step 1; Equate equation 1 and 2 together

`\begin{gathered} \text{ x - 5 = x}^2\text{ - 2x - 9} \\ \text{ x}^2\text{ - 2x - 9 - x + 5 = 0} \\ \text{ x}^2\text{ -2x - x - 4= 0} \\ \text{ x}^2\text{ - 3x - 4= 0} \end{gathered}`

Step 2; factorize the above quadratic equation above

`\begin{gathered} \text{ x}^2\text{ - 3x - 4 = 0} \\ \text{ x}^2\text{ -4x + x -4 = 0} \\ \text{ x\lparen x - 4\rparen + 1 \lparen x - 4\rparen= 0} \\ \text{ \lparen x - 4\rparen = 0 or \lparen x + 1 \rparen = 0} \\ \text{ x = 4 or x = -1} \end{gathered}`

Step 3; Find the values of y by substituting the values of x into equation 1

`\begin{gathered} \text{ y = x - 5} \\ \text{ x1 = 4 and x2 = -1} \\ \text{ y1 = 4 - 5} \\ \text{ y1 = -1} \\ \\ \text{ y2 = x2 - 5} \\ \text{ y2 = -1 - 5} \\ y2\text{ = -6} \end{gathered}`

Therefore, we have (4, -1) or (-1, -6)