systems of equations

Question

the difference of two numbers is 3. Their sum is 13. find the numbers.

Answer 1

Let the bigger number be x and the smaller number be y. We have:

x - y = 3 --- (1)
x + y = 13 --- (2)

From (1), we have:

y = x - 3 --- (3)

Substituting (3) into (2), we have:

x + (x - 3) = 13
x + x - 3 = 13
2x = 13 + 3
2x = 16
x = 16 / 2
x = 8

Substituting x = 8 into (3), we have:

y = 8 - 3
y = 5

Hence, x = 8 and y = 5.

Answer 2

3x +2y =7

4x +5y =14