Question
Question 6 of 10 Solve the system of equations below. \[ \begin{aligned} 4 x+y=16 \\ 2 x+3 y=-2\end{aligned} \] \[ \begin{array}{l}\text { A. }(5,-4) \\ \text { B. }(4,-5) \\ \text { c. }(5,4) \\ \text { D. }(-5,4)\end{array} \]
Ask by Delgado Wang. in the United States
Feb 26,2025
Upstudy AI Solution
Tutor-Verified Answer
Answer
The solution to the system is (5, -4), which is option A.
Solution
We start with the system:
4x + y = 16 (1)
2x + 3y = -2 (2)
Step 1: Solve equation (1) for y.
y = 16 - 4x
Step 2: Substitute y = 16 - 4x into equation (2):
2x + 3(16 - 4x) = -2
Step 3: Expand and simplify:
2x + 48 - 12x = -2
-10x + 48 = -2
Step 4: Isolate x:
-10x = -2 - 48
-10x = -50
x = (-50)/(-10) = 5
Step 5: Substitute x = 5 back into y = 16 - 4x:
y = 16 - 4(5) = 16 - 20 = -4
Thus, the solution to the system is (5, -4).
The correct answer is A.
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Simplify this solution Bonus Knowledge
To solve the system of equations, we will use substitution or elimination. Let's start by solving for \(y\) from the first equation: \[ y = 16 - 4x \] Now we can substitute this expression for \(y\) into the second equation: \[ 2x + 3(16 - 4x) = -2 \] Distributing the 3 gives: \[ 2x + 48 - 12x = -2 \] Combining like terms: \[ -10x + 48 = -2 \] Next, we'll isolate \(x\): \[ -10x = -2 - 48 \] \[ -10x = -50 \] \[ x = 5 \] Now that we have \(x\), we can substitute it back into the first equation to find \(y\): \[ 4(5) + y = 16 \] \[ 20 + y = 16 \] \[ y = 16 - 20 \] \[ y = -4 \] Thus, the solution to the system of equations is \((5, -4)\), which corresponds to option A.
