Question

Find where the lines intersect. Y = x - 5 & y = -2x + 1

Answer 1

We want to find where the two lines intersect

$\begin{gathered} y=x-5 \\ \text{and} \\ y=-2x+1 \end{gathered}$

Solution

We will subtitute equation 1 into equation 2 ( since y is already made the subject)

From (1)

$y=x-5$

Put into (2), from (2)

$\begin{gathered} y=-2x+1 \\ x-5=-2x+1 \\ \text{collect like terms} \\ x+2x=1+5 \\ 3x=6 \\ x=\frac{6}{3} \\ x=2 \end{gathered}$

We substitute the value of x into (1)

From (1)

$\begin{gathered} y=x-5 \\ y=2-5 \\ y=-3 \end{gathered}$

Therefore, the point is intersection is (2, -3) or the line intersect at x = 2 and y = -3

The graph below further show this claim