Question

solve the following system of linear equations by addition. indicate whether the given system of linear equations has one solution, has no solution, or has an infinite number of solutions. if the system has one solution, find the solution.\\\

$$\begin{cases}7x + 7y = 28\\\\2y = -2x + 10\\end{cases}$$

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answer\
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\\(\bigcirc\\) one solution \\((\quad,\quad)\\)\
\\(\bigcirc\\) no solution\
\\(\bigcirc\\) infinite number of solutions

Explanation:

Step1: Simplify the first equation

Divide the first equation \(7x + 7y = 28\) by 7:
\(\frac{7x}{7}+\frac{7y}{7}=\frac{28}{7}\)
\(x + y = 4\)

Step2: Simplify the second equation

Rewrite the second equation \(2y=-2x + 10\) in standard form. Add \(2x\) to both sides:
\(2x+2y = 10\)
Divide by 2:
\(\frac{2x}{2}+\frac{2y}{2}=\frac{10}{2}\)
\(x + y = 5\)

Step3: Analyze the two simplified equations

We have \(x + y = 4\) and \(x + y = 5\). Subtract the first from the second:
\((x + y)-(x + y)=5 - 4\)
\(0=1\), which is a contradiction.

Answer:

No Solution