Question

Anyone know this algebra problem?

Answer 1

Equation 1) 6x + 7y = 59
Equation 2) 4x + 5y = 41

We're simply just trying to find the value of "x" & "y"

So, we must try to cancel out either "x" or "y"

Our first step :

Multiply all of equation 1 by 2.

1) 2(6x + 7y = 59)

Simplify.

1) 12x + 14y = 118

Then, multiply all of equation 2 by 3.

2) 3(4x + 5y = 41)

Simplify.

2) 12x + 15y = 123

1) 12x + 14y = 118

Notice how BOTH equations 1 & 2 have "12x" in the equation.

Now, we can subtract the equations from one another.

Subtract the "x" with the "x", the "y" with the "y", and the numbers with the numbers. (sorry, that was slightly confusing)

12x - 12x = 0

15y - 14y = 1y → y

123 - 118 = 5

Therefore, y = 5

Now, we simply plug in 5 for y in our original equation 1.

1) 6x + 7y = 59

6x + 7(5) = 59

Simplify.

6x + 35 = 59

Subtract 35 from both sides.

6x = 59 - 35

Simplify.

6x = 24

Divide both sides by 6.

x = 4

&

y = 5

So, your final answer is : (4, 5)

~Hope I helped!~ :)

Answer 2

Hello there!

To solve for this, we need to figure out the value for each variable. Both of these values must work for each of the variables in both equations.

Although I've already solved for the variables in my head, I'll just use them as the example for this anyways.

6x + 7y = 59
Let's plug in "4" for x, and "5" for y.
6(4) + 7(5)
24 + 35
59. < -- this value works, but let's continue with our second equation just to be sure.

4x + 5y = 41
Once again, let's plug in "4" for x, and "5" for y.
4(4) + 5(5)
16 + 25
41. < -- this value also works, so we now have our answers.

The value for 'x' is "4", and the value for 'y' is "5".

I hope this helps! Have a great day!