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nlexa [21]
2 years ago
13

Solve using the method of elimination and determine if the system has 1 solution, no solutions, or infinite solutions

Mathematics
1 answer:
Minchanka [31]2 years ago
8 0

\begin{array}{rrrrr} 10x&-&18y&=&2\\ -5x&+&9y&=&-1 \end{array}~\hfill \implies ~\hfill \stackrel{\textit{second equation }\times 2}{ \begin{array}{rrrrr} 10x&-&18y&=&2\\ 2(-5x&+&9y&)=&2(-1) \end{array}} \\\\[-0.35em] ~\dotfill\\\\ \begin{array}{rrrrr} 10x&-&18y&=&2\\ -10x&+&18y&=&-2\\\cline{1-5} 0&+&0&=&0 \end{array}\qquad \impliedby \textit{another way of saying \underline{infinite solutions}}

if we were to solve both equations for "y", we'd get

10x-18y=2\implies 10x-2=18y\implies \cfrac{10x-2}{18}=y\implies \cfrac{5}{9}x-\cfrac{1}{9}=y \\\\\\ -5x+9y=-1\implies 9y=5x-1\implies y=\cfrac{5x-1}{9}\implies y = \cfrac{5}{9}x-\cfrac{1}{9}

notice, the 1st equation is really the 2nd in disguise, since both lines are just pancaked on top of each other, every point in the lines is a solution or an intersection, and since both go to infinity, well, there you have it.

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3 years ago
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Four less than three times a number is three more than two times the<br> number. What is the number?
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Hello!

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Look at the first part. "Four less than three times a number". The first thing being done here is the <u>three times a number.</u> This would be 3n, as it is 3 times n. Now, there is the <u>four less</u> part. You would therefore have to subtract 4 from 3n, to get 3n - 4.

Now the second part. "Is three more than two times the number". The first thing being done here is the <u>two times the number</u>. That would be 2n. The next is "is three more than". If the other side is three more than 2n, then you must add 3 to 2n to make them equivalent. Therefore, it would be 2n + 3.

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3 years ago
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3 years ago
Add $50 million and 179.7 billion,
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