Question

Use substitution to solve the system 5x-3y=23 2x+y=7

Answer 1

Because "y" is + in 2x+y=7, let's subtract 2x from both sides and end up with an expression for y:  y = 7 - 2x.  Substituting this into 5x - 3y = 23, 

5x - 3(7 - 2x) = 23.  Multiply out -3(7 - 2x):

5x - 21 + 6x = 23.  Combining 5x and 6x, 11x - 21 = 23, or 11x = 44.

Thus, x = 4.  Since y = 7 - 2x, subst. x = 4 results in the value of y:

y = 7 - 2(4) = 7 - 8 = -1.

The solution is (4,-1).