Question

What is the solution to the system of equations?

Answer 1

As with a system of equations, call them A and B in order to keep them straight.

A: x + y = 7

B: x = y + 3

Because in B we have x on one on one side and not x on the other, substitution is the way to go. Substitute equation B into equation A.

x + y = 7 Equation A

y + 3 + y = 7 Putting B into A

2y + 3 = 7 Collect like terms

2y = 4 Subtract 3 on both sides

y = 2 divide both sides by 2

With y = 2 we can substitute that back into an original equation. Choose B.

x = y + 3

x = 2 + 3

x = 5

Thus x = 5 and y = 2, or (5, 2) is the solution of this system.