Problem

Given the system of equations: $\left\{\begin{array}{l}-8 x-8 y=-20 \\ 24 x+24 y=60\end{array}\right.$ How many solutions does it have? No Solution Infinitely Many Solutions One Solution What is the solution? Note: If there is not a single solution, write "DNE" in each box. Question Help: D Post to forum

Solution

Step 1 :Given the system of equations: \(\left\{\begin{array}{l}-8 x-8 y=-20 \\ 24 x+24 y=60\end{array}\right.\)

Step 2 :To determine the number of solutions for the system of equations, we need to check if the equations are equivalent, parallel, or intersecting.

Step 3 :If the equations are equivalent, there will be infinitely many solutions.

Step 4 :If the equations are parallel and not equivalent, there will be no solution.

Step 5 :If the equations intersect at a single point, there will be one solution.

Step 6 :The second equation is a multiple of the first equation, which means they are equivalent lines.

Step 7 :Therefore, there are infinitely many points of intersection.

Step 8 :\(\boxed{\text{Infinitely Many Solutions}}\)

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