Math  /  Algebra

Questiony=5x+24xy=0\begin{array}{l} y=5 x+2 \\ 4 x-y=0 \end{array}
Is (2,12)(2,12) a solution of the system?

Studdy Solution

STEP 1

What is this asking? We're checking if the point (2,122, 12) makes *both* equations true! Watch out! Make sure you check *both* equations, not just one!

STEP 2

1. Check the first equation.
2. Check the second equation.

STEP 3

Let's **substitute** x=2x = 2 and y=12y = 12 into the first equation, y=5x+2y = 5x + 2.
This gives us 12=52+212 = 5 \cdot 2 + 2.
We're doing this to see if the left side equals the right side when we plug in our xx and yy values.

STEP 4

Let's **simplify** the right side: 52+2=10+2=125 \cdot 2 + 2 = 10 + 2 = 12.
So, we have 12=1212 = 12.
Awesome! This means the point (2,12)(2, 12) works for the first equation.

STEP 5

Now, let's **substitute** x=2x = 2 and y=12y = 12 into the second equation, 4xy=04x - y = 0.
This gives us 4212=04 \cdot 2 - 12 = 0.
Again, we're checking if the left side equals the right side with our given point.

STEP 6

Let's **simplify** the left side: 4212=812=44 \cdot 2 - 12 = 8 - 12 = -4.
So, we have 4=0-4 = 0.
Uh oh!
This isn't true!

STEP 7

Since the point (2,12)(2, 12) works for the first equation but *not* the second equation, it's *not* a solution to the system.
The answer is no!

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