the sum of three times a number and two times another number is 14. negative three times the first number minus four times the second number is 10. what is the first number

Answer 1

3x + 2y = 14

+(-3x - 4y = 10)

-2y = 24

y = -12

x = 12.67

Answer 2

Let x = the first number

y = the second number

Eq. I: 3x + 2y = 14

Eq. II: -3x - 4y = 10

Add these two equations together and we get:

-2y = 24

y = 24/-2

y = -12

Use either equation with this value of y to solve for x, which is the number we are looking for. Let's use Eq. I:

3x +2y = 14

3x = 14 - 2y

3x = 14 - 2(-12)

3x = 14 - (-24)

3x = 14 + 24

3x = 38

x = 38/3

x = 12 2/3

Check that both equations are satisfied with these values. You will find that they are, so then the answer is x = 12 2/3.