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Math  /  Algebra

Question㸚. Is (3,−4)(3,-4) a solution to this system of equations? y=−4x−8y=−4\begin{array}{l} y=-4 x-8 \\ y=-4 \end{array} yes no

Studdy Solution

STEP 1

1. We are given a system of two equations and need to determine if the point (3,−4)(3, -4) is a solution.
2. A point (x,y)(x, y) is a solution to a system of equations if it satisfies all equations in the system.

STEP 2

1. Substitute the point (3,−4)(3, -4) into the first equation.
2. Check if the point satisfies the first equation.
3. Substitute the point (3,−4)(3, -4) into the second equation.
4. Check if the point satisfies the second equation.
5. Determine if the point is a solution to the system.

STEP 3

Substitute the point (3,−4)(3, -4) into the first equation y=−4x−8y = -4x - 8.
Substitute x=3x = 3 and y=−4y = -4:
−4=−4(3)−8 -4 = -4(3) - 8

STEP 4

Calculate the right-hand side of the equation:
−4=−12−8 -4 = -12 - 8 −4=−20 -4 = -20
Since −4≠−20-4 \neq -20, the point (3,−4)(3, -4) does not satisfy the first equation.

STEP 5

Substitute the point (3,−4)(3, -4) into the second equation y=−4y = -4.
Substitute y=−4y = -4:
−4=−4 -4 = -4

STEP 6

Since −4=−4-4 = -4, the point (3,−4)(3, -4) satisfies the second equation.

STEP 7

The point (3,−4)(3, -4) does not satisfy the first equation but satisfies the second equation. Therefore, it is not a solution to the system of equations.
The answer is no\boxed{\text{no}}.

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