Question

Use the elimination method to solve the following system of equations. 2x + y = 7 6x - y = 9 Select the correct choice below and, if necessary, fill in the answer box to complete your choice. O A. The solution is (Simplify your answer. Type an ordered pair.) B. There are infinitely many solutions. O C. There is no solution.Can someone help please I'm confused

Answer 1

Solve by elimination;

$\begin{gathered} 2x+y=7---(1) \\ 6x-y=9---(2) \\ Add\text{ equation (2) to equation (1)} \\ (2x+6x)+(y+\lbrack-y\rbrack)=7+9 \\ 8x+(y-y)=16 \\ 8x+0=16 \\ 8x=16 \\ \text{Divide both sides by 8} \\ x=2 \\ \text{Substitute for the value of x into equation (1)} \\ 2x+y=7 \\ 2(2)+y=7 \\ 4+y=7 \\ \text{Subtract 4 from both sides} \\ 4-4+y=7-4 \\ 0+y=3 \\ y=3 \end{gathered}$

The answer therefore is x = 2, y = 3

As an ordered pair, that would be

(2, 3)