Question

Question 2(Multiple Choice Worth 4 points) (08.02)A pair of equations is shown below. x + y = 5 y = one halfx + 2 If the two equations are graphed, at what point do the lines representing the two equations intersect? (2, 5) (5, 2) (2, 3) (3, 2)

Answer 1

`(2,3)`

Explanation:

The first equation is
`x+y=5`

The second equation is
`y=(1)/(2)x+2`

When we graph these two equations, they will meet at a point which represent the solution of the two equations.

We can solve the two equations simultaneously to determine their point of intersection.

Let us substitute the second equation into the first equation to get;

`x+(1)/(2)x+2=5`

Multiply through by 2 to get;

`2x+x+4=10`

Group similar terms to obtain;

`2x+x=10-4`

Simplify;

`3x=6`

Divide both sides by 3;

`\Rightarrow x=2`

Put
`x=2` into the second equation;

`y=(1)/(2)(2)+2`

`\Rightarrow y=1+2`

`\Rightarrow y=3`

Therefore the graphs of the two functions intersect at (2,3)

See graph in attachment.