Question

he instructions state.." here is a system of equations y=2x+3 y=x-1graph the system. then write its solution. bother that you can also answer "no solution" or "infinitely many" solutions.

Answer 1

`\begin{gathered} y=2x+3 \\ y=x-1 \end{gathered}`

To grpah the given sytem of linear equations:

1. Find two points (x,y) in each line (each equation):

- First equation:

`y=2x+3`

Find the value of x when y is 0:

`\begin{gathered} 0=2x+3 \\ -3=2x \\ -(3)/(2)=x \\ \\ \text{ }-1.5=x \end{gathered}`

First point (-1.5, 0)

Find the value of y when x is 0:

`\begin{gathered} y=2(0)+3 \\ y=3 \end{gathered}`

Second point (0,3)

- Second equation:

`y=x-1`

Find the value of x when y is 0:

`\begin{gathered} 0=x-1 \\ 1=x \end{gathered}`

First point (1,0)

Find the valueo of y when x is 0:

`\begin{gathered} y=0-1 \\ y=-1 \end{gathered}`

Second point (0, -1)

2. Graph each line using the two corresponding points:

Put the points in the plane and draw a line that passes through it.

First equation, points: (-1.5, 0) and ( 0,3)

Second equation, points: (1,0) and (0,-1)

3. Find the solution for the system.

The solution is the point where the line crosses: (-4,-5)