Math  /  Algebra

Questiony=2x1y=3x4\begin{array}{l}y=2 x-1 \\ y=3 x-4\end{array}

Studdy Solution

STEP 1

What is this asking? Find the mystery xx and yy values that make *both* of these equations true! Watch out! Don't forget that the solution must satisfy *both* equations simultaneously.

STEP 2

1. Set the equations equal
2. Solve for xx
3. Substitute and solve for yy

STEP 3

Since both equations are already solved for yy, we can set the right-hand sides equal to each other.
This creates a *new* equation where we can solve for xx!

STEP 4

2x1=3x42x - 1 = 3x - 4

STEP 5

We want to get all the xx terms on one side.
Subtracting 2x2x from both sides helps us do just that! 2x12x=3x42x2x - 1 - 2x = 3x - 4 - 2x 1=x4-1 = x - 4

STEP 6

Now, let's isolate xx by adding 4 to both sides! 1+4=x4+4-1 + 4 = x - 4 + 4 3=x3 = xSo, our mystery xx value is **3**!

STEP 7

We can use either of the original equations to solve for yy.
Let's use the first one because it looks a little simpler!

STEP 8

Remember, we found that x=3x = \mathbf{3}.
Let's plug that in! y=231y = 2 \cdot \mathbf{3} - 1

STEP 9

y=61y = 6 - 1 y=5y = 5 Awesome! Our mystery yy value is **5**!

STEP 10

The solution is x=3x = \mathbf{3} and y=5y = \mathbf{5}.
This means that if you plug in x=3x = \mathbf{3} and y=5y = \mathbf{5} into *both* of the original equations, they'll both be true!

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