Question

solve the system of equations. if the system has no solution, say that it is inconsistent. graph the lines of the system.\

$$\begin{cases}x + y = 9\\\\x - y = 5\\end{cases}$$

\select the correct choice below and, if necessary, fill in any answer boxes within your choice.\\a. the solution is x = 7 and y = 2. (type integers or simplified fractions.)\\b. there are infinitely many solutions. using ordered pairs, they can be expressed as \\{(x,y)| x = \square, y is any real number\\}.\\(\text{simplify your answer. type an expression using } y \text{ as the variable as needed.}\\)\\c. the system is inconsistent.\use the graphing tool to graph the lines.

Explanation:

Step1: Add the two equations

We have the system:

$$\begin{cases} x + y = 9 \\ x - y = 5 \end{cases}$$

Adding the two equations together: $(x + y) + (x - y) = 9 + 5$.
Simplifying the left side: $x + y + x - y = 2x$.
Simplifying the right side: $14$. So we get $2x = 14$.

Step2: Solve for x

Divide both sides of $2x = 14$ by 2: $x=\frac{14}{2}=7$.

Step3: Substitute x into one equation

Substitute $x = 7$ into the first equation $x + y = 9$: $7 + y = 9$.
Subtract 7 from both sides: $y = 9 - 7 = 2$.

Answer:

A. The solution is \( x = 7 \) and \( y = 2 \).