Question $2x + 5y = 13$

Studdy Solution

STEP 1

What is this asking? We're looking for numbers $x$ and $y$ that make the equation $2x + 5y = 13$ true! Watch out! There are lots of possible answers here, not just one.
Don't get stuck thinking there's only one perfect pair of $x$ and $y$ !

STEP 2

1. Explore the equation
2. Find a solution
3. Find another solution!

STEP 3

Let's rewrite the equation to make it easier to work with.
We'll get $y$ by itself!
We start with $2x + 5y = 13$ . Subtract $2x$ from both sides to get $5y = 13 - 2x$ .
Now, divide both sides by $5$ to isolate $y$ .
This gives us $y = \frac{13 - 2x}{5}$ .
Awesome!

STEP 4

Now, let's pick a value for $x$ and see what $y$ we get!
Let's start simple with $x = 0$ .
Plugging that into our equation gives us $y = \frac{13 - 2 \cdot 0}{5} = \frac{13}{5}$ .
So one solution is $x = 0$ and $y = \frac{13}{5}$ !

STEP 5

Let's try another value for $x$ just for fun!
How about $x = 1$ ?
Substituting $x = 1$ into our equation gives us $y = \frac{13 - 2 \cdot 1}{5} = \frac{11}{5}$ .
So another solution is $x = 1$ and $y = \frac{11}{5}$ !
See? Lots of answers!

STEP 6

We found two solutions!
One is $x = 0$ and $y = \frac{13}{5}$ .
Another is $x = 1$ and $y = \frac{11}{5}$ .
There are infinitely many more, but these two are great examples!

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