Question

Graph these equations: x+2y=6, y=-1/2x+4 How many solutions does the system of equations have?

Answer 1

The system has no solution

Explanation:

we have

`x+2y=6`

Isolate the variable y

`2y=-x+6`

Divide by 2 both sides

`y=-(x)/(2)+3` ---> equation A

`y=-(x)/(2)+4` ---> equation B

Compare the equations

Equation A and equation B have the same slope and different y-intercept

Remember that

If two lines have the same slope, then the lines are parallel

The solution of the system is the intersection point both graphs

In this problem, the lines don't intersect, therefore, the system has no solution

using a graphing tool

The graph in the attached figure