How do you solve this system of equations: 4x - 3y = 39 and 3x + y = 39?

3 Answers
Dec 12, 2017

See a solution process below:

Explanation:

Step 1) Solve the second equation for y:

3x + y = 39

-color(red)(3x) + 3x + y = -color(red)(3x) + 39

0 + y = -3x + 39

y = -3x + 39

Step 2) Substitute (-3x + 39) for y in the second equation and solve for x:

4x - 3y = 39 becomes:

4x - 3(-3x + 39) = 39

4x + (-3 xx -3x) + (-3 xx 39) = 39

4x + 9x + (-117) = 39

4x + 9x - 117 = 39

(4 + 9)x - 117 = 39

13x - 117 = 39

13x - 117 + color(red)(117) = 39 + color(red)(117)

13x - 0 = 156

13x = 156

(13x)/color(red)(13) = 156/color(red)(13)

(color(red)(cancel(color(black)(13)))x)/cancel(color(red)(13)) = 12

x = 12

Step 3) Substitute 12 for x in the solution to the second equation at the end of Step 1 and calculate y:

y = -3x + 39 becomes:

y = (-3 xx 12) + 39

y = -36 + 39

y = 3

The Solution Is: x = 12 and y = 3 or (12, 3)

Dec 12, 2017

x=12, y=3

Explanation:

Let's start by solving for a single variable. 3x+color(red)(y)=39 looks easy, since color(red)(y) doesn't have a coefficient to make things messy. So, let's rewrite that as

color(red)(y)=39-3x

Now let's substitute

4x-3color(red)(y)=39

4x-3(color(red)(39-3x))=39

4x-117+9x = 39

13x = 156

color(blue)(x=12)

color(white)(0)

Now that we have x, let's solve for y:

color(white)(0)

3(color(blue)(x))+y=39

3(color(blue)(12))+y=39

color(red)(y=3)

. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

Now let's double check our math here:

We say that x=12 and that y=3

4x-3y=39

4(12)-3(3) should equal 39, if our math is right

48-9

39

We were right! 39 is 39, and so x must equal 12 and that y does equal 3.

Another way we could have checked that is graphed the two functions and see where they intercepted, which is at the point (12, 3).

So either way, we can see that we are correct! Nice work

Dec 12, 2017

x=12
y=3

Here's how I did it!

Explanation:

First you want to pick one of your two equations and a variable you want to isolate in it. I'm going to pick 3x+y=39 because it'll be pretty easy to solve for y.

3x+y=39

y=-3x+39

Perfect! Now we have a value for y. We can plug this into our second equation, 4x-3y=39, and solve for a value of our other variable, x.

4x-3y=39

4x-3(-3x+39)=39

4x+9x-117=39

13x-117=39

13x=156

x=12

Great! Now that we have a numerical value for x, we can plug that back into our first equation, 3x+y=39.

3x+y=39

3(12)+y=39

36+y=39

y=3

There we go!