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

Answer:

solution is (-2,4)

Step-by-step explanation:

$x+y=2$

$y=\frac{1}{2} x+5$

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

$y=\frac{1}{2} x+5$

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)