Question

Graph the system below and write its solution.2x+y=-6y=1/4x+3Note that you can also answer "No solution" or "Infinitely many" solutions.

Answer 1

System of Equations

Given the system of equations:

2x + y = -6

y = 1/4x + 3

It's required to solve it by graphing.

The graph of a line can be drawn by only knowing two points of it.

To graph the first equation, solve for y:

y = -2x - 6

Now give x two values. For example, x = -5 and x = -1.

For x = -5:

y = -2(-5) - 6

y = 10 - 6 = 4

Point (-5, 4)

For x = -1:

y = -2(-1) - 6

y = 2 - 6 = -4

Point (-1, -4)

With these points, we can graph the first equation. The graph will be shown below in red.

Now graph the second equation:

y = 1/4x + 3

For x = -8

y = 1/4(-8) + 3

y = -2 + 3 = 1

Point (-8, 1)

For x = 0:

y = 1/4(0) + 3

y = 0 + 3 3

y = 3

Point (0,3)

The second line is drawn in blue below.