Question

I need help with my math

Answer 1

We are given the equations

`y=(3)/(2)x+2`

and

`y=\text{ -2x -5}`

and told to identify the solution set. We will first graph both equations and check:

-if they cross at only one point, then there is only one solution

-if they don't cross, then there are no solutions, and

-if they have the same graph, then they have infinitely many solutions.

Since they are lines, we can define the plot by finding two points that are on the line.

For the first line, let us find the values of y when x=0 and x=2. So we have

`y=(3)/(2)\cdot0+2=2`

and

`y=(3)/(2)\cdot2+2=3+2=5`

This gives us the points (0,2) and (2,5) .

Now, for the second line, we will find the values of y when x=0 and when x=2. So we have

`y=\text{ -2}\cdot0\text{ -5= -5}`

and

`y=\text{ -2}\cdot2\text{ -5= -9}`

This gives us the points (0,-5) and (2, -9). So now, we proceed to plot this points

Note that the lines cross at one point, so there is one solution. A more precise drawing of the system would show that they cross at the point (-2,-1). So the solution set is the point (-2,-1).