Question

Solve the system by graphing: $\left\{\begin{array}{l}y=3x-1\\ 6x-2y=6\end{array}\right.$

Short answer

The system of equations $\left\{\begin{array}{l}y=3x-1\\ 6x-2y=6\end{array}\right.$has no solution and it can be seen in the graph as,

Step-by-step solution

Step 1. Given Information.

We are given a system of equations $\left\{\begin{array}{l}y=3x-1\\ 6x-2y=6\end{array}\right.$and we need to find its solution by graphing.

Step 2. Graph the first equation.

The equation $y=3x-1$is in slope-intercept form, so its slope is 3 and its $y$intercept is $-1$.

So its graph is given as

Step 3. Graph the second equation on the same rectangular coordinate system.

Solving the equation $6x-2y=6$for $y$we get,

$\begin{array}{rcl}6x-2y-6x& =& 6-6x\\ -2y& =& -6x+6\\ \frac{-2y}{-2}& =& \frac{-6x+6}{-2}\\ y& =& 3x-3\end{array}$

So the slope of the line is $3$and its $y$intercept is $-3$.

So its graph can be drawn on the same plane as

Step 4. Identify the solution to the system.

• From the graph, it can be seen that the lines are parallel.
• Since no point is on both lines, there is no ordered pair that makes both equations true.
• There is no solution to the given system.