What is the solution of the following systems?

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pumpkin1625

High School

What is the solution of the following systems?

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gmany

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$\left\{\begin{array}{ccc}3x+3y=10\\-9x-9y=-30&|\text{divide both sides by 3}\end{array}\right\\\underline{+\left\{\begin{array}{ccc}3x+3y=10\\-3x-3y=-10\end{array}\right}\qquad|\text{add both sides of equations}\\.\qquad\qquad\ \ \ 0=0\\\\3x+3y=10\ \ \ |-3x\\3y=10-3x\ \ \ |:3\\y=\dfrac{10-3x}{3}\\\\Answer:\\\text{It is dependent system of equations}\\\text}Infinite solutions}\\\\\left\{\begin{array}{ccc}x\in\mathbb{R}\\y=\dfrac{10-3x}{3}\end{array}\right$
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tramserran

3x + 3y = 10 ⇒ 3( 3x + 3y = 10) ⇒ 9x + 9y = 30
-9x - 9y = -30 ⇒ 1(-9x - 9y = -30) ⇒ -9x - 9y = -30
0 + 0 = 0
TRUE
Since it makes a true statement, there are infinite solutions.
When graphing, they are the same line.
Answer: Infinite Solutions
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