Algebra 1 word problems

Question

When you subtract two numbers, you get 9. Find the larger number if the sum

is 17.

Answer 1

Let x = larger number; y = smaller number

x-y=9

x+y=17

Solve the system of equations by adding them to get 2x=26. So x=13.

Then plug in x=13 into one of the equations to get y=4.

So, the larger number is 13 (x=13)

Answer 2

x is larger no., y is smaller.

So x - y = 9

Sum is 17, so x + y = 17.

You can solve the system of equations by subtraction:

x - y = 9

x + y = 17

-2y = -8 so y = -8/-2 = 4 If y = 4, x is 17 - 4 = 13. Answer: y = 4; x = 13

Check: 13 - 4 = 9 (OK)

13 + 4 = 17 (OK)

Also use substitution: x = 9 + y Substitute in 2nd eqn: 9 + y + y = 17 -> 9 + 2y = 17 -.> 2y = 8 -> y = 4

Then x = 17 - y -> x = 17 - 4 = 13