Two numbers, x and y, when added together equal 9 and equal -5 when subtracted

Question

What would be the addition and subtraction equation and what would be the value of x and value of y.

Answer 1

The quickest way of solving this is by adding the equations in rows to cancel out a variable:

x+y=9

x-y=-5

+ ----------

2x = 4 ----> x = 2

then just plug in x to any equation:

2 + y = 9 -----> y = 7

Answer 2

For word problems such as this you want to write out what's happening first. X and y, when added together equal 9

x + y = 9

x and y, equal -5 when subtracted

x - y = -5

Now we can use one equation to solve for the other. Let's take x - y = -5 we can transform that into

x = y - 5

We can now substitute that into our first equation x + y = 9

x + y = 9

x = y - 5

y - 5 + y = 9

2y - 5 = 9

Now we need to isolate the variable

2y - 5 = 9

2y = 14

Now we can solve for y

y = 7

If we plug this back into our original substitution (x = y - 5)

x = y - 5

x = 7 - 5

x = 2

Our final answers are

x = 2

y = 7

x + y = 9

x - y = -5