Question

Determine the solution of the system of equations represented by the lines in the graph. Check your solution by substituting into bothequations3x + 3y = 9x - y = -5

Answer 1

Solution is (-1, 4)

Step-by-step explanation:
`\begin{gathered} \text{Given equations:} \\ 3x\text{ + 3y = 9 ... (1)} \\ x\text{ - y = -5 ... (2)} \end{gathered}`

The graph of both equations have been given. The point of interscetion is the solution of the graphs

We check the graph for the point where they meet:

The point of intersection is (-1, 4)

We need to check if we picked the right point by substituting the y and x values in each of the equations:

`\begin{gathered} 3x+3y=9 \\ x\text{ = -1, y = 4} \\ 3(-1)\text{ + 3(4) = 9} \\ -3\text{ + 12 = 9} \\ 9\text{ = 9} \\ \text{left hand side is equal to right hand side, so it is a solution} \end{gathered}`
`\begin{gathered} x\text{ - y = -5} \\ x\text{ = -1},\text{ y =4} \\ -1\text{ - 4 = -5} \\ -5\text{ = -5} \\ \text{left hand side is equal to right hand side},\text{ so it is a solution} \end{gathered}`