3times a 1st number increased by a 2nd number is 2.Twice the 1st number increased by the second number is 7.?

Question

I need to find the numbers and I am having trouble finding them! Can some one please help?

Answer 1

1st number: x
2nd number: y

3x + y = 2
2x + y = 7
----------------
x = -5
y = 17

The first number is -5
The second number is 17

Answer 2

Let a be the first number.
Let b be the second number.

From the statements you can form two equations:
3a + b = 2
2a + b = 7

Subtracting these two equations:
a = 2 - 7
a = -5

Solving for b:
2(-5) + b = 7
-10 + b = 7
b = 17

So the numbers are -5 and 17

You can also solve the two equations using substitution.

3a + b = 2
2a + b = 7

Solve the first equation for b:
b = 2 - 3a

Substitute this into the second equation
2a + (2 - 3a) = 7
2a + 2 - 3a = 7
-a + 2 = 7
-a = 5
a = -5

Then solve for b as usual.
b = 2 - 3a
b = 2 - 3(-5)
b = 2 - (-15)
b = 2 + 15
b = 17

Either way the answers come out to -5 and 17

You should double-check the answers.

"3 times the first number (-15) increased by the second number (17) is 2"
True, because -15 + 17 = 2

"Twice the first number (-10) increased by the second number (17) is 7"
True because -10 + 17 = 7

Therefore the two numbers are -5 and 17