Question 615001
the point is (6,2)
it lies on the line:
-x - 8y = -22.
if it was a solution to the system of linear equations, then the point would be at the intersection of the 2 lines of those equations.
if it was at the intersection of those 2 lines, it would be common to both lines.
it would therefore have to be on both lines.
if it was on both lines, then both equations would be true when you replaced x and y with 6 and 2.
let's see what happens if we do that.
first equation is -x - 8y = -22
this becomes:
-(6) - 8(2) = -6 - 16 = -22
it is definitely on the first line.
second equation is -7x + 3y = -36
this becomes:
-7(6) + 3(2) = -42 + 6 = -36
looks like it's on the second line too.
since the point is common to both equations, it is a simultaneous solution of the system of those equations
you can graph these equations as shown below:
{{{graph(600,600,-10,10,-10,10,(-22+x)/-8,(7x-36)/3)}}}
you can see that the lines intersect at the point (6,2).