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Math  /  Algebra

Question2) (−2,0);8x−3y=−1650=−9x−2y(-2,0) ; \begin{array}{l}8 x-3 y=-16 \\ 50=-9 x-2 y\end{array}

Studdy Solution

STEP 1

1. The problem involves determining whether the point (−2,0)(-2, 0) is a solution to the given system of linear equations.
2. The system of equations is: $ \begin{align*} 8x - 3y &= -16 \\ 50 &= -9x - 2y \end{align*} \]

STEP 2

1. Substitute the point (−2,0)(-2, 0) into the first equation.
2. Check if the point satisfies the first equation.
3. Substitute the point (−2,0)(-2, 0) into the second equation.
4. Check if the point satisfies the second equation.
5. Determine if the point is a solution to the system of equations.

STEP 3

Substitute the point (−2,0)(-2, 0) into the first equation 8x−3y=−168x - 3y = -16.
8(−2)−3(0)=−16 8(-2) - 3(0) = -16

STEP 4

Simplify the expression to check if it holds true:
−16=−16 -16 = -16
The point (−2,0)(-2, 0) satisfies the first equation.

STEP 5

Substitute the point (−2,0)(-2, 0) into the second equation 50=−9x−2y50 = -9x - 2y.
50=−9(−2)−2(0) 50 = -9(-2) - 2(0)

STEP 6

Simplify the expression to check if it holds true:
50=18 50 = 18
The point (−2,0)(-2, 0) does not satisfy the second equation.

STEP 7

Since the point (−2,0)(-2, 0) does not satisfy both equations, it is not a solution to the system of equations.
The point (−2,0)(-2, 0) is not a solution to the system of equations.

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