Question

What is the solution of the system x − 3y = –13 and 5x + 7y = 34?

Answer 1

(1/2, 9/2)

Explanation:

Write the system as a column (not as a row of characters):

x − 3y = –13 and 5x + 7y = 34 =>

x − 3y = –13

5x + 7y = 34

Let's eliminate x using the method of addition and subtraction. Multiply all terms of the first row by -5:

-5x + 15y = 65

5x + 7y = 34

The sum of these two equations is

22y = 99, and so

y = 9/2

Substituting 9/2 or y in the first equation, we get:

x - 3(9/2) = -13, which simplifies to:

x = 27/2 - 13, or

x = 27/2 - 26/2, or x = 1/2

Then the solution is (1/2, 9/2)