Studdy AI Logo
Math  /  Algebra

Question3x+4y=−23x=3y+1x=□y=□\begin{array}{l}3 x+4 y=-23 \\ x=3 y+1 \\ x=\square \\ y=\square\end{array}

Studdy Solution

STEP 1

What is this asking? We've got two equations with two mystery numbers, xx and yy, and we need to find what those mystery numbers are! Watch out! Make sure to keep track of your xx’s and yy’s, they can get mixed up really easily!

STEP 2

1. Substitute
2. Solve for yy
3. Solve for xx

STEP 3

Alright, let's **kick things off** by looking at our second equation: x=3y+1x = 3y + 1.
This tells us what xx is in terms of yy.
It's like a secret code!
Let's use this secret code in our first equation.
Wherever we see an xx in the first equation, we're going to swap it out with 3y+13y + 1.

STEP 4

So, our first equation 3x+4y=−233x + 4y = -23 **transforms** into 3(3y+1)+4y=−233(3y + 1) + 4y = -23.
See how we swapped the xx for (3y+1)(3y + 1)?
This is called **substitution**, like substituting one player for another in a game!

STEP 5

Now, let's **crack this code** and find yy!
First, we **distribute** the 3 in the equation 3(3y+1)+4y=−233(3y + 1) + 4y = -23, which gives us 9y+3+4y=−239y + 3 + 4y = -23.
Remember, distributing means multiplying the 3 by each term inside the parentheses.

STEP 6

Next, let's **combine** our yy terms: 9y+4y9y + 4y gives us 13y13y.
So, our equation becomes 13y+3=−2313y + 3 = -23.

STEP 7

We want to get yy all by itself, so let's **subtract** 3 from both sides of the equation.
This gives us 13y+3−3=−23−313y + 3 - 3 = -23 - 3, which simplifies to 13y=−2613y = -26.
Remember, we're adding −3-3 to both sides to get rid of the +3+3 on the left side, since 3+(−3)=03 + (-3) = 0.

STEP 8

Finally, we **divide** both sides by 13 to isolate yy.
So, 13y=−2613y = -26 becomes 13y13=−2613\frac{13y}{13} = \frac{-26}{13}, which gives us y=−2y = \mathbf{-2}.
We found our first mystery number!

STEP 9

Now that we know y=−2y = -2, we can **plug it back** into our secret code equation: x=3y+1x = 3y + 1.

STEP 10

**Substituting** −2-2 for yy, we get x=3(−2)+1x = 3(-2) + 1.

STEP 11

This simplifies to x=−6+1x = -6 + 1, which gives us x=−5x = \mathbf{-5}.
We found our second mystery number!

STEP 12

x=−5x = -5 y=−2y = -2

Was this helpful?

Studdy solves anything!

banner

Start learning now

Download Studdy AI Tutor now. Learn with ease and get all help you need to be successful at school.

ParentsInfluencer programContactPolicyTerms
TwitterInstagramFacebookTikTokDiscord