Question

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

x+y=2
y=1/2x+5
x+ y=2
-1/2x+y =5

Subtracting the two equations;
3/2x=-3
x=-2
Replacing in the first equation;
-2+y=2
y=4
They would intersect at (-2, 4)

Answer 2

solution is (-2,4)

Explanation:

`x+y=2`

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

LEts graph both equations.

`x+y=2` solve for y

`y=-x+2`

Make a table to graph the equation

x y=-x+2

0 y=2

1 y=1

Graph the points (0,2) and (1,1) . then extend the line that connects two points

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

x y=(1/2)x+5

0 y=5

2 y=6

Graph the points (0,5) and (2,6) . then extend the line that connects two points

The graph is attached below

Both lies intersects at (-2,4)