Question

Solve the system graphically and check the solution. 2x-3y=6. 2x-3y=12

Answer 1

Given

2x - 3y = 6

2x - 3y = 12

Graph the two equations

Graphing 2x - 3y = 6

Use x = 0 and y = 0 as a point

`\begin{gathered} \text{IF }x=0,\text{ THEN} \\ 2x-3y=6 \\ 2(0)-3y=6 \\ -3y=6 \\ y=-2 \\ \text{We have point }(0,-2) \\ \\ \text{IF }y=0,\text{ THEN} \\ 2x-3y=6 \\ 2x-3(0)=6 \\ 2x=6 \\ x=3 \\ \text{We have point }(3,0) \end{gathered}`

Plot the two point (0,-2) and (3,0) and connect a line, the graph for 2x - 3y = 6 is

Graphing 2x - 3y = 12

Use the same process as above

`\begin{gathered} \text{IF }x=0,\text{ THEN} \\ 2(0)-3y=12 \\ -3y=12 \\ y=-4\text{ plot point }(0,-4) \\ \\ \text{IF }y=0,\text{ THEN} \\ 2x-3(0)=12 \\ 2x=12 \\ x=6\text{ plot point }(6,0) \end{gathered}`

Draw in the previous graph, and connect the two points for 2x-3y = 12

Since the two equations are parallel, there is no intersection in the line and thus there are no solutions to the system.