The sum of five times a number and twice a second number is 18, but the difference of three times the first number and seven times the second number is -22. Find the two numbers using the elimination method.
A. -2 and -4
B. -2 and 4
C. 2 and -4
D. 2 and 4

Question

The sum of five times a number and twice a second number is 18, but the difference of three times the first number and seven times the second number is -22. Find the two numbers using the elimination method.
	A.	-2 and -4
	B.	-2 and 4
	C.	2 and -4
	D.	2 and 4

thomas5267 · Answer

From the question, we know there is a relationship between the two numbers.  Lets call the first one A and the second one B.

Try to use mathematical formula to express the following two relationship:

1. The sum of five times a number and twice a second number is 18.
2. The difference of three times the first number and seven times the second number is -22.

anonymous · Answer

5x + 2y = 18
3x - 7y = -22

Is that correct @thomas5267

thomas5267 · Answer

Correct.  Do you know how to use the elimination method?

anonymous · Answer

Uhh not really @thomas5267

thomas5267 · Answer

For example:
$$
\begin{align*}
4x + 5y &= 14 \
-4x - 3y &= -10
\end{align*}
$$
The elimination method is when you add or subtract one equation to another equation to eliminate one variable, like this.
$$
\begin{align*}
(4x+5y)+(-4x-3y)&=(14)+(-10) \
2y&=4 \
y&=2
\end{align*}
$$

anonymous · Answer

Ohhhh ok

anonymous · Answer

ugh im still kinda confused @thomas5267

thomas5267 · Answer

Hint: $5x+2y=18$ and $15x+6y=54$ is the same.

anonymous · Answer

So is the answer C?

anonymous · Answer

@thomas5267

anonymous · Answer

The sum of five times a number and twice a second number is 18, but the difference of three times the first number and seven times the second number is -22. Find the two numbers using the elimination method.

Let the number be x and second number be y. So:
5x + 2y = 18
But 3x - 7y = -22

Now you have two equations. To solve by elimination method, you need to bring one of the coefficients (either of x or y) equal for both equations then cancel.
5x + 2y = 18 Multiply everything by 3
3x - 7y = -22 Multiply everything by 5

15x + 6y = 54
15x - 35y = -110
Subtract
15x will get cancelled.
So,
41y = 164
y = 164/41 = 4
So, y = 4
Substitute this value of y=4 in equation 1.

5x + 2(4)  =18
5x + 8 = 18
5x = 18 - 8
5x = 10
x = 10/5 =2

So, x = 2 and y = 4.

That is D.