The graphs lof the lines 3x + 4y = 2, 5x - y = 11
and x + ky = -2 all contain the same point.
We'll use the first two equations to find x and y,
then substitute those into the third equation to
find k.
Multiply the second equation by 4 so we can
eliminate the y terms by adding the two equations.
4 * (5x - y) = 4 * 11
20x - 4y = 44
Now, add them.
3x + 4y = 2
20x - 4y = 44
-------------------
23x = 46
23x = 46
x = 2
Use that in the second equation to find y.
5 * 2 - y = 11
10 - y = 11
-y = 11 - 10 = 1
y = -1
Put both x and y into the third equation.
x + ky = -2
2 + k * (-1) = -2
2 - k = -2
-k = -2 -2 = -4
k = 4