Questions: Solve the system algebraically. 23. -2x - y = -14 3x - y = 11 a. (-4, -5) c. (-5, -4) b. (5, 4) d. (4, 5)

Solve the system algebraically. 23. -2x - y = -14 3x - y = 11 a. (-4, -5) c. (-5, -4) b. (5, 4) d. (4, 5)
Transcript text: Solve the system algebraically. 23. $\left\{\begin{array}{l}-2 x-y=-14 \\ 3 x-y=11\end{array}\right.$ a. $(-4,-5)$ c. $(-5,-4)$ b. $(5,4)$ d. $(4,5)$
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Solution

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Solution Steps

Step 1: Write down the system of equations

The given system of equations is: {−2x−y=−143x−y=11 \begin{cases} -2x - y = -14 \\ 3x - y = 11 \end{cases}

Step 2: Subtract the first equation from the second to eliminate y y

Subtract the first equation from the second: (3x−y)−(−2x−y)=11−(−14) (3x - y) - (-2x - y) = 11 - (-14) Simplify: 3x−y+2x+y=11+14 3x - y + 2x + y = 11 + 14 5x=25 5x = 25

Step 3: Solve for x x

Divide both sides by 5: x=255=5 x = \frac{25}{5} = 5

Step 4: Substitute x=5 x = 5 into the first equation to solve for y y

Substitute x=5 x = 5 into the first equation: −2(5)−y=−14 -2(5) - y = -14 Simplify: −10−y=−14 -10 - y = -14 Add 10 to both sides: −y=−4 -y = -4 Multiply both sides by -1: y=4 y = 4

Step 5: Verify the solution

The solution is (5,4) (5, 4) , which corresponds to option b.

Final Answer

The correct answer is B.

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