What is the solution to the system?
line 1
x y
–1 –2
1 2
line 2
x y
–2 10
4 1
( , )

So we convert them to slope-intercept form which is y=mx+b where m=slope and b=y intercept

first line
(-1,-2)
(1,2)
slope=(y1-y2)/(x1-x2)
x1=-1
y1=-2
x2=1
y2=2
subsitute
(-2-2)/(-1-1)=-4/-2=4/2=2
slope=2
subsitute
y=2x+b
subsitute another point
(1,2)
x=1
y=2 is one solution
2=2(1)+b
2=2+b
subtract 2 from both sides
0=b
the equation is y=2x+0 or y=2x

other equation
(-2,10)
(4,1)
x1=-2
y1=10
x2=4
y2=1
subsitute
(10-1)/(-2-4)=9/-6=-3/2
slope=-3/2
y=-3/2x+b
subisute points that work
(-2,10)
x=-2
10=y is one solution
10=-3/2(-2)+b
10=6/2+b
10=3+b
subtract 3
7=b
y=-3/2x+7

we have y=-3/2x+7 and y=2x
subsitute
2x=y=-3/2x+7
2x=-3/2x+7
add 3/2x to both sides
2x+3/2x=7
2x=4/2x
4/2x+3/2x=7
7/2x=7
multiply both sides by 2/7
x=14/7
x=2
subisute for y
y=2x
y=2(2)
y=4

the point is (2,4)