The given system of equations is
[tex]\begin{gathered} y+5x=3\rightarrow(1) \\ y-x=6\rightarrow(2) \end{gathered}[/tex]To solve it graphically, we have to draw each line, then take the point of intersection of them as a solution
To draw a line we need 2 points on it, then we will put a value of x, then find its corresponding value of y
For the 1st line:
Let x = 0
[tex]\begin{gathered} y+5(0)=3 \\ y=3 \end{gathered}[/tex]The first point is (0, 3)
Let x = 1
[tex]\begin{gathered} y+5(1)=3 \\ y+5=3 \\ y+5-5=3-5 \\ y=-2 \end{gathered}[/tex]The second point is (1, -2)
For the 2nd line
Let x = 0
[tex]\begin{gathered} y-0=6 \\ y=6 \end{gathered}[/tex]The first point is (0, 6)
Let x = 1
[tex]\begin{gathered} y-1=6 \\ y-1+1=6+1 \\ y=7 \end{gathered}[/tex]The second point is (1, 7)
Let us draw the 2 lines
The green line represents equation (1)
The purple line represents equation (2)
The two lines intersected at point (-0.5, 5.5)
The solution of the system is (-0.5, 5.5)
To check the solution substitute x by -0.5 and y by 5.5, the answer must equal the right side
[tex]\begin{gathered} 5.5+5(-0.5)=5.5-2.5=3 \\ \text{LHS}=\text{RHS} \end{gathered}[/tex][tex]\begin{gathered} 5-5-(-0.5)=5.5+0.5=6 \\ \text{LHS}=\text{RHS} \end{gathered}[/tex]The solution satisfies both equations
