Questions: Find the general solution of the following system of equations. -2x + 7y = -6 -4x + 14y = -12 Select the correct answer below: (x, 2x/7 - 5/7) (x, 7x/2 + 3) (x, 2x/7 - 6) (x, 7x/2 - 6) (x, 7x/2 + 5)

Find the general solution of the following system of equations. -2x + 7y = -6 -4x + 14y = -12 Select the correct answer below: (x, 2x/7 - 5/7) (x, 7x/2 + 3) (x, 2x/7 - 6) (x, 7x/2 - 6) (x, 7x/2 + 5)
Transcript text: Question Find the general solution of the following system of equations. \[ \left\{\begin{aligned} -2 x+7 y & =-6 \\ -4 x+14 y & =-12 \end{aligned}\right. \] Select the correct answer below: $\left(x, \frac{2 x}{7}-\frac{5}{7}\right)$ $\left(x, \frac{7 x}{2}+3\right)$ $\left(x, \frac{2 x}{7}-6\right)$ $\left(x, \frac{7 x}{2}-6\right)$ $\left(x, \frac{7 x}{2}+5\right)$
failed

Solution

failed
failed

Solution Steps

Step 1: Analyze the system of equations

The given system of equations is: \[ \left\{\begin{aligned} -2x + 7y & = -6 \\ -4x + 14y & = -12 \end{aligned}\right. \] Notice that the second equation is a multiple of the first equation. Specifically, the second equation is obtained by multiplying the first equation by 2.

Step 2: Determine the nature of the system

Since the second equation is a scalar multiple of the first, the two equations represent the same line. This means the system has infinitely many solutions, and the general solution can be expressed in terms of one variable.

Step 3: Express \( y \) in terms of \( x \)

From the first equation: \[ -2x + 7y = -6 \] Solve for \( y \): \[ 7y = 2x - 6 \\ y = \frac{2x}{7} - \frac{6}{7} \] Thus, the general solution is: \[ \left(x, \frac{2x}{7} - \frac{6}{7}\right) \]

Step 4: Compare with the given options

The correct answer is: \[ \left(x, \frac{2x}{7} - \frac{6}{7}\right) \] This matches the third option provided: \[ \left(x, \frac{2x}{7} - 6\right) \]

Final Answer

The correct answer is C.

Was this solution helpful?
failed
Unhelpful
failed
Helpful

Questions asked by other users

failedAnswered
Find the first four terms of the sequence given by the following. [ an=6 cdot(-3)^n-1, quad n=1,2,3 ldots ]
failedAnswered
Systems of Linear Equations Solving a (2 times 2) system of linear equations that is inconsistent or consistent... Two systems of equations are given below. For each system, choose the best description of its solution. If applicable, give the solution. System A [ beginarrayr x+2 y=8 -x-2 y=8 endarray ] The system has no solution. The system has a unique solution: [ (x, y)=, ] The system has infinitely many solutions. They must satisfy the following equation: [ y= ] System B [ beginaligned x+3 y =9 -x =3 y-9 endaligned ] The system has no solution. The system has a unique solution: [ (x, y)=, ] The system has infinitely many solutions. They must satisfy the following equation: [ y= ]
failedAnswered
Evelyn is a hard worker and has a good job and a modest, but nice house. However, Evelyn checks her social media accounts regularly, and follows several celebrities. When she sees them getting facials with real gold and buying expensive cars and houses, she thinks about her own belongings and feels inadequate. This illustrates: downward social comparison upward social comparison class-based bias self-serving bias
failedAnswered
Use the References to access important values if needed for this question. Write a net ionic equation to show why solid potassium hydroxide, KOH(s), forms a basic solution when it dissolves in water.
failedAnswered
Which of the following shapes are quadrilaterals? Choose 2 answers: A B C D