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:
{−2x−y=−143x−y=11
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+145x=25
Step 3: Solve for x
Divide both sides by 5:
x=525=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.