Question

What is the solution of the following systems?

Answer 1

`\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=(10-3x)/(3)\\\\Answer:\\\text{It is dependent system of equations}\\\text}Infinite solutions}\\\\\left\{\begin{array}{ccc}x\in\mathbb{R}\\y=(10-3x)/(3)\end{array}\right`

Answer 2

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