Two times a number plus three times another number equals 13. The sum of the two numbers is 7. What are the numbers?

Answer 1

Let x and y be the 2 numbers.

Given x+y = 7 and 2x+3y = 13.

Since x+y = 7, it follows that x = 7-y.

Use this in the 2nd equation:

2(7 - y) + 3y = 13

Expand and combine like terms

14 - 2y + 3y = 13

14 + y = 13

Subtract 14 from both sides to find

y = 13-14 = -1

x+y = 7 ==> x+ (-1) = 7 ==> x=8

CHECK: 2x + 3y = 2*8 + 3*(-1) = 16 - 3 = 13.

Answer 2

From the question we know:

2x+3y=13

x+y=7. ->. y=7-x

substitute into the first equation:

2x+3(7-x)=13

-x+21=13

x=8

plug that into equation 2+y=7

y=5