Problem

Use substitution to solve the system. \[ \begin{aligned} 3 x+7 y & =-42 \\ 4 x-y & =6 \end{aligned} \] Select the correct choice below and, if necessary, fill in the answer box to complete your choice. A. The solution is $\square$. (Type an,ordered pair.) B. There àre infinitely many solutions. C. There is no solution.

Solution

Step 1 :The system of equations is given as follows: \[\begin{aligned} 3 x+7 y & =-42 \\ 4 x-y & =6 \end{aligned}\]

Step 2 :First, solve the second equation for y to get \(y = 4x - 6\).

Step 3 :Substitute \(y = 4x - 6\) into the first equation to get \(3x + 7(4x - 6) = -42\), which simplifies to \(31x - 42 = -42\).

Step 4 :Solve the equation \(31x - 42 = -42\) to get \(x = 0\).

Step 5 :Substitute \(x = 0\) back into the equation \(y = 4x - 6\) to get \(y = -6\).

Step 6 :So, the solution to the system of equations is \(\boxed{(0, -6)}\).

From Solvely APP
Source: https://solvelyapp.com/problems/4XLterLeld/

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