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Math  /  Algebra

Question(7,−4);9b+4a=−86a+5b−42=0(7,-4) ; \begin{array}{l}9 b+4 a=-8 \\ 6 a+5 b-42=0\end{array}

Studdy Solution

STEP 1

1. We are given a system of two linear equations with two variables aa and bb.
2. The point (7,−4)(7, -4) is likely a solution to the system, meaning it satisfies both equations.
3. We need to verify if (7,−4)(7, -4) is a solution or find the values of aa and bb that satisfy both equations.

STEP 2

1. Substitute the given point into both equations.
2. Solve the first equation for one variable.
3. Substitute the expression from Step 2 into the second equation.
4. Solve for the remaining variable.
5. Verify the solution by substituting back into the original equations.

STEP 3

Substitute the given point (7,−4)(7, -4) into both equations. The equations are:
9b+4a=−8 9b + 4a = -8 6a+5b−42=0 6a + 5b - 42 = 0
Substitute a=7a = 7 and b=−4b = -4 into the first equation:
9(−4)+4(7)=−8 9(-4) + 4(7) = -8
Calculate:
−36+28=−8 -36 + 28 = -8
This simplifies to:
−8=−8 -8 = -8
The point satisfies the first equation.

STEP 4

Substitute the given point (7,−4)(7, -4) into the second equation:
6(7)+5(−4)−42=0 6(7) + 5(-4) - 42 = 0
Calculate:
42−20−42=0 42 - 20 - 42 = 0
This simplifies to:
0=0 0 = 0
The point satisfies the second equation.
The point (7,−4)(7, -4) satisfies both equations, confirming that it is a solution to the system.

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