Question

Find the numbers whose sum is 9, if

three times the first number increased
by two times the second number
equals 22.

Answer 1

Let x be the first number and y be the second number. We know from the given information that:

3x + 2y = 22

We also know that the sum of the two numbers is 9, so:

x + y = 9

To find the values of x and y, we can use a method such as substitution. We can solve one equation for one variable, and then substitute that expression into the other equation.

We can solve the first equation for y:

y = (22 - 3x)/2

Then substitute this expression for y into the second equation:

x + (22 - 3x)/2 = 9

Simplifying and solving for x, we get:

2x + 22 = 18

x = -2

Now that we know x = -2, we can substitute it back into the first equation to find y:

3(-2) + 2y = 22

y = 4

So the two numbers are x = -2, y = 4.