Question

Please Help! A pair of equations is shown below. x + y = 2 y = one halfx + 5 If the two equations are graphed, at what point do the lines representing the two equations intersect? (4, −2) (−2, 4) (2, 5) (5, −2)

Answer 1

(- 2, 4 )

Explanation:

Given the 2 equations

x + y = 2 → (1)

y =
`(1)/(2)` x + 5 → (2)

Substitute y =
`(1)/(2)` x + 5 into (1)

x +
`(1)/(2)` x + 5 = 2 ( multiply through by 2 to clear the fraction )

2x + x + 10 = 4

3x + 10 = 4 ( subtract 10 from both sides )

3x = - 6 ( divide both sides by 3 )

x = - 2

Substitute x = - 2 into (1) and evaluate for y

- 2 + y = 2 ( add 2 to both sides )

y = 4

Solution is (- 2, 4 )

Answer 2

(-2,4)

Explanation:

First, put x+y=2 into slope-intercept form: y=-x+2

Second, set the to equations equal to each other: -x+2=1/2x+5

Then, add x to both sides: -x+x+2=1/2x+x+5 to get: 2=3/2x+5

Next, subtract 5 from both sides: 2-5=3/2x+5-5, to get -3=3/2x

Finally, to get the x-value, divide both sides by 3/2: -3(2/3)=3/2x(2/3), to get x=-2

Lastly, substitute -2 for x into one of the equations to find y:

x+y=2

-2+y=2

add 2 to both sides: -2+2+y=2+2, to get y=4

The solution is (-2,4)