Questions: 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. $(4,5)$

Solution

Solution Steps

Step 1: Write down the system of equations

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

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

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

Step 3: Solve for $ x $

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

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

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

Step 5: Verify the solution

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