Math  /  Algebra

Questiony=x2y=3x+4\begin{array}{l} y=x-2 \\ y=3 x+4 \end{array}
Is (4,2)(4,2) a solution of the system? Choose 1 answer: (A) Yes (B) No

Studdy Solution

STEP 1

What is this asking? We need to check if the point (4,24,2) 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

We're given x=4x = 4 and y=2y = 2.
Let's plug these values into the first equation, y=x2y = x - 2.
This becomes 2=422 = 4 - 2.

STEP 4

We have 2=422 = 4 - 2, which simplifies to 2=22 = 2.

STEP 5

Since 2=22 = 2 is a true statement, the point (4,24,2) satisfies the first equation.
Awesome!

STEP 6

Now, let's plug x=4x = 4 and y=2y = 2 into the second equation, y=3x+4y = 3x + 4.
This gives us 2=34+42 = 3 \cdot 4 + 4.

STEP 7

We have 2=34+42 = 3 \cdot 4 + 4, which simplifies to 2=12+42 = 12 + 4, and further to 2=162 = 16.

STEP 8

Uh oh! 2=162 = 16 is *not* a true statement.
This means the point (4,24,2) does *not* satisfy the second equation.

STEP 9

Since the point (4,24,2) works for the first equation but *not* the second, it's *not* a solution to the system of equations.
The answer is (B) No.

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