Question

Please help with this math problem so my son can understand better I have attached the image. For some reason he keeps getting it incorrect cause he's not sure were the point should be placed on the graph please help.

Answer 1

Step 1

Choose input values for x for both equations based on his graph. The x-values on his graph sheet range from -10 to 10. we will choose; -10, -8,0,4 and 10.

Step 2

Input these x-values in the first equation and get values for the output y.

`\begin{gathered} 3x+y=6 \\ \text{Transforming the above equation we will have; y=6-3x} \\ y=6-3x \\ x=-10 \\ y=6-3(-10) \\ y=6+30 \\ y=36 \\ \text{First point(-10,36)} \end{gathered}`
`\begin{gathered} \text{If x=-8} \\ y=6-3(-8) \\ y=6+24 \\ y=30 \\ \text{second point}(-8,30) \end{gathered}`
`\begin{gathered} \text{If x=0} \\ y=6-3(0_{}) \\ y=6 \\ \text{Third point(0,6)} \end{gathered}`
`\begin{gathered} \text{If x=4} \\ y=6-3(4) \\ y=6-12 \\ y=-6 \\ \text{Fourth point(4,-6)} \end{gathered}`
`\begin{gathered} \text{If x=10} \\ y=6-3(10) \\ y=6-30=-24 \\ \text{fifth point(10,-24)} \\ \end{gathered}`

Step 3

Find similar points using the same x values for line 2, the second equation

`\begin{gathered} -3x-4y=12 \\ -4y=12+3x \\ -(4y)/(-4)=(12)/(-4)+((3x)/(-4)) \\ y=-3-(3x)/(4) \end{gathered}`
`\begin{gathered} \text{If x=-10, points are }(-10,4.5) \\ \text{If x=-8 points are (-8,}3) \\ \text{if x =0 points are (}0,-3) \\ \text{if x=4 points are (4,}-6) \\ \text{if x=10 points are (10},-10.5) \end{gathered}`