For what ordered pair $(a,b)$ are there infinite solutions $(x,y)$ to the system\begin{align} 3ax+3y&=5b,\\ 2x+y&=5. \end{align}

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For what ordered pair $(a,b)$ are there infinite solutions $(x,y)$ to the system\begin{align*} 3ax+3y&=5b,\\ 2x+y&=5. \end{align*}

Guest Jul 30, 2022

CPhill · Answer 1 · 2022-07-30T11:42:23

3ax + 3y = 5b

2x + y = 5 multiply through by 3 → 6x + 3y = 15

To have infinite solutions the equations must be the same ......this implies that

3a = 6 and 5b = 15

a = 2 b = 3

For what ordered pair $(a,b)$ are there infinite solutions $(x,y)$ to the system\begin{align*} 3ax+3y&=5b,\\ 2x+y&=5. \end{align*}