Math Help URGENT

Question

Write a system of equations and solve by either method, substitution or elimination. Show your work to get full or partial credit.

The sum of two numbers is 26 and the difference between three times the larger and twice the smaller is 18.

Hint: Let x= the larger and y = the smaller number.

Answer 1

Hi Grace!

Word based problems can be confusing, but once you get used to a few familiar words and phrases it should help you out. So, there are two numbers, x (larger) and y (smaller).

The sum of the two numbers equals 26. This means that when x is added to y, you get 26.

Your first equation is x+y=26

The next equation sounds a little more difficult. Let's break it down:

the difference between three times the larger and twice the smaller is 18.

We can gain a few bits of knowledge from this:

1. we will be subtracting
2. The larger number, x, has a coefficient of 3
3. The smaller number, y, has a coefficient of 2
4. We will be subtracting in the form x-y. This is due to the order of the mentioned variables

From there, we can write the equation:

3x-2y=18

And now we have our 2 equations:

x+y=26

3x-2y=18

To solve, let's use substitution. Because there is an equation with variables that don't have coefficients, it will be the easier to work with.

x+y=26

Now, solve for y or x

x=26-y

Plug the value of x into the equation:

3(26-y)-2y=18

78-3y-2y=18

78-5y=18

Now, combine terms so that you can solve for y

5y=60

y=12

Now, we can plug the new value of y into either equation (I will plug it into the first, but it's always good to plug it into both and solve for x)

x+12=26

x=14

your answers are x=14 and y=12

Answer 2

To write the system of equations, the skill you need is translating a word problem into an equation.

"The sum of two numbers is 26" translates to:

x + y = 26

"the difference between three times the larger and twice the smaller is 18" becomes

3x - 2y = 18

Next, you can use substitution or elimination to combine these equations and solve them.

For me, substitution seems simpler here, so we will solve for y in the first equation,

(x + y) - x = (26) - x

y = 26 - x

Then we can substitute it into the second equation.

3x - 2(26 - x) = 18

simplifying, we can solve for x.

x = 14

Now it is easy to substitute x into either equation and solve for y. Make sure to check your answers in both equations!