Question

Solve by graphing 6X + 3y equals 12 8x + 4y equals 24

Answer 1

The system of equation has no solution.

Step-by-step explanation:

Given the system of equation;

`\begin{gathered} 6x+3y=12\text{ -----1} \\ 8x+4y=24\text{ -----2} \end{gathered}`

We want to solve the system of equation by graphing.

Let us derive two points on each equation and graph;

`\begin{gathered} 6x+3y=12\text{ -----1} \\ at\text{ x=0} \\ y=(12)/(3)=4 \\ (0,4) \\ \\ at\text{ x=2} \\ y=0 \\ (2,0) \end{gathered}`

for the second equation;

`\begin{gathered} 8x+4y=24\text{ -----2} \\ at\text{ x=0;} \\ y=(24)/(4)=6 \\ (0,6) \\ \\ at\text{ x=3;} \\ y=0 \\ (3,0) \end{gathered}`

Let us locate the points on the graph and plot;

The graph of the system of equation is shown above.

We can observe that the lines are parallel to each other and cannot meet.

Therefore, since the graph of the equations are parallel to each other, then the system of equation has no solution.