Problem

Use substitution to solve the system. \[ \begin{array}{c} 3 x-3 y=10 \\ -2 x+y=-4 \end{array} \] Select the correct choice below and, if necessary, fill in the answer box to complete your choice. A. The solution is (Simplify your answer. Type an ordered pair.) B. There are infinitely many solutions. C. There is no solution.

Solution

Step 1 :Given the system of equations: \[\begin{array}{c} 3 x-3 y=10 \\ -2 x+y=-4 \end{array}\]

Step 2 :Express one variable in terms of the other from one equation. From the first equation, we can express y in terms of x: \[y = x - \frac{10}{3}\]

Step 3 :Substitute this expression into the second equation: \[-2x + (x - \frac{10}{3}) = -4\]

Step 4 :Solve this equation for x to get: \[x = \frac{2}{3}\]

Step 5 :Substitute x = \frac{2}{3} back into the first equation to solve for y: \[y = -\frac{8}{3}\]

Step 6 :Final Answer: The solution is \(\boxed{(\frac{2}{3}, -\frac{8}{3})}\)

From Solvely APP
Source: https://solvelyapp.com/problems/24291/

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