Question

In the following exercises, solve the system of equations by using graphing.

$$\begin{gathered} 3x^2-y=0 \\ y=2x-1 \end{gathered}$$

Short answer

System of equations have no solution.

Step-by-step solution

Given information 

Given two equations are

$$\begin{gathered} 3x^2-y=0 \\ y=2x-1 \end{gathered}$$

Graph first equation 

Given equation is

$$\begin{gathered} 3x^2-y=0 \\ 3x^2=y \\ y=3x^2 \end{gathered}$$

we find out the vertex using formula

$$\begin{gathered} x=\frac{-b}{2a} \\ a=3,b=0 \\ x=\frac{-0}{2\left(3\right)}=0 \\ y=3x^2 \\ y=3{\left(0\right)}^2=0 \\ vertexis(0,0) \end{gathered}$$

The value of a=3, a is positive. so the graph of parabola goes up .

x and y intercept is (0,0)

Now graph the parabola

Graph the second equation 

$y=2x-1$

substitute x =0 and find out y intercept

substitute y=0 and find out x intercept

$$\begin{gathered} y=2x-1 \\ x=0 \\ y=2\left(0\right)-1 \\ y=-1 \\ yinterceptis(0,-1) \\ y=0 \\ 0=2x-1 \\ 1=2x \\ x=\frac{1}{2} \\ xinterceptis(0.5,0) \end{gathered}$$

Graph the intercepts and connect it by a line .

Graph both the equations in same plane

Intersection 

Both the graphs does not intersects.

So , no solution for these system of equations