Question

Please help linear equations please see attached picture to understand better

Answer 1

Given

$\begin{gathered} 4x+2y=18 \\ y=-2x+9 \end{gathered}$

Part A

Checking for

$\begin{gathered} (4,1) \\ x=4 \\ y=1 \\ 4x+2y=18\ldots\text{equation 1} \\ \text{and } \\ y=-2x+9\ldots\text{equation 2} \\ substitute\text{ for x=4 and y=1 in equation 1} \\ 4(4)+2(1)=18 \\ 16+2=18 \\ 18=18 \\ substitute\text{ for x=4 and y=1 in equation }2 \\ 1=-2(4)+9 \\ 1=-8+9_{}_{} \\ 1=1 \end{gathered}$

Yes (4,1) is a solution

Part B

$\begin{gathered} x=-5\text{ and y=19} \\ 4x+2y=18 \\ 4(-5)+2(19)=18 \\ -20+38=18 \\ 18=18 \\ \text{and} \\ y=-2x+9 \\ 19=-2(-5)+9 \\ 19=10+9 \\ 19=19 \end{gathered}$

Yes (-5,19) it is a solution

Part C

$\begin{gathered} x=5\text{ and y=}-3 \\ 4x+2y=18 \\ 4(5)+2(-3)=18 \\ 20-6=18 \\ 14\ne18 \end{gathered}$

No (5,-3) is not a solution

Part D

$\begin{gathered} x=6\text{ and y=0} \\ 4x+2y=18 \\ 4(6)+2(0)=18 \\ 24+0=18 \\ 24\ne18 \end{gathered}$

No (6,0) it is not solution

The final answer