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}}`

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