You're given a system of linear equations and are charged with the task of finding a single solution to this system, if there is one. In other words, you must come up with the coordinates of the point of intersection of the graphs of these two lines.
y= -3x +4
y= 2x -11
Note that we can immediately elimiinate y by setting these two equations equal to one another: y= -3x +4 = y= 2x - 11. By subtracting y from both sides, we end up with -3x +4 = 2x - 11.
Combining like terms we get 5x on the right and 15 on the left.
Solving for x, x = 15/5 = 3. Now that we know x = 3, subst. 3 for x in the 2nd equation: y = 2x - 11 becomes y = 2(3) - 11, or y = 6 - 11, or y = -5.
The solution to your system of linear equations is the point (3, -5).
You should verify that this point satisfies both of the given equations.