Question
\( \begin{array}{l}4 x+2 y=12 \\ -4 x-5 y=6\end{array} \) What is the solution \( (x, y) \) to the given system of equations? Choose 1 answer:
Ask by Mccarthy Tucker. in the United States
Feb 19,2025
Upstudy AI Solution
Tutor-Verified Answer
Answer
The solution is (6, –6).
Solution
Let's solve the system:
1) 4x + 2y = 12
2) –4x – 5y = 6
Step 1: Solve the first equation for x:
4x = 12 – 2y
x = 3 – (y/2)
Step 2: Substitute x into the second equation:
–4(3 – (y/2)) – 5y = 6
Simplify:
–12 + 2y – 5y = 6
–12 – 3y = 6
Step 3: Solve for y:
–3y = 18
y = –6
Step 4: Substitute y back to find x:
x = 3 – ((-6)/2) = 3 + 3 = 6
Thus, the solution is (x, y) = (6, –6).
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Simplify this solution Beyond the Answer
To solve the system of equations, let's start with the first equation: 1. From the first equation \(4x + 2y = 12\), we can simplify it to \(2x + y = 6\) by dividing the whole equation by 2. 2. Now let's solve for \(y\): \(y = 6 - 2x\). 3. Substitute \(y\) into the second equation \(-4x - 5y = 6\): \(-4x - 5(6 - 2x) = 6\). 4. Simplifying that, we get: \(-4x - 30 + 10x = 6\), \(6x - 30 = 6\), \(6x = 36\), \(x = 6\). 5. Now substitute \(x = 6\) back into \(y = 6 - 2x\): \(y = 6 - 2(6) = 6 - 12 = -6\). So the solution to the system of equations is \((6, -6)\).
