Question

a system of equations is shown:
4x = -3y + 17
3x - 4y = -6
what is the solution to this system of equations?
(-2, -3)
(3, 2)
(2, 3)
(-3, -2)

Explanation:

Step1: Rearrange first equation

Rewrite \(4x = -3y + 17\) as \(4x + 3y = 17\).

Step2: Use elimination method

Multiply the first equation \(4x + 3y = 17\) by 4: \(16x + 12y = 68\).
Multiply the second equation \(3x - 4y = -6\) by 3: \(9x - 12y = -18\).

Step3: Add the two new equations

\((16x + 12y) + (9x - 12y) = 68 + (-18)\)
\(25x = 50\)
\(x = 2\).

Step4: Substitute x=2 into first equation

Substitute \(x = 2\) into \(4x + 3y = 17\):
\(4(2) + 3y = 17\)
\(8 + 3y = 17\)
\(3y = 9\)
\(y = 3\).

Step5: Check the solution

Check \((2, 3)\) in both equations:
First equation: \(4(2) = -3(3) + 17\) → \(8 = -9 + 17\) → \(8 = 8\) (true).
Second equation: \(3(2) - 4(3) = -6\) → \(6 - 12 = -6\) → \(-6 = -6\) (true).

Answer:

C. (2, 3)