Question

At how many points do the graphs of the equations y = 2x + 5 and y = x² - 2x- 7 intersect?

Answer 1

Answer: $\Large\boxed{\text{Two Points}}$

Step-by-step explanation:

Given a system of equation

$1)~y=2x+5$

$2)~y=x^2-2x-7$

Substitute the 2) equation for the y value of the 1) equation

$2x+5=x^2-2x-7$

Subtract [ 2x + 5 ] on both sides

$2x+5-(2x+5)=x^2-2x-7-(2x+5)$

$x^2-2x-7-2x-5=0$

$x^2-4x-12=0$

Cross multiply the equation

$x~~~~~~~~~~~~~~~-6$

$x~~~~~~~~~~~~~~~2$

$(x-6)(x+2)=0$

$x=6~\text{or}~x=-2$

Since there are 2 x values, this represents that there are $\Large\boxed{\text{Two}}$ intersecting points

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The following is EXTRA information for the question if you need to find the points of intersection

Substitute the x values into one of the equations to find the y value

$\text{When}~x=6:$

$y=2x+5$

$y=2(6)+5$

$y=12+5$

$y=17$

$\large\boxed{(6,17)}$

$\text{When}~x=-2:$

$y=2x+5$

$y=2(-2)+5$

$y=-4+5$

$y=1$

$\large\boxed{(2,~1)}$

Graph the equations to check the solutions

Please refer to the attachment below for the graph