ACT Math : How to find the solution for a system of equations

Study concepts, example questions & explanations for ACT Math

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Example Questions

Example Question #41 : How To Find The Solution For A System Of Equations

What is the solution to the system of linear equations defined by:

Give your answer as an ordered pair.

Possible Answers:

Correct answer:

Explanation:

There are many methods to finding the solution of a system of linear equations: graphing, elimination, substitution, matrix manipulations; we'll use subsitution.

Since both equations are equal to , we can use substitution to set them equal to each other and solve for x:

Now we plug the value we just found for  into either equation (it doesn't matter, check both if you're unsure)

Thus we get the ordered pair: 

Example Question #2021 : Act Math

Sales for a business were  more the second year than the first, and sales for the third year were double the sales for the second year. If sales for the third year were , what were sales, in millions of dollars, for the first year?

Possible Answers:

Correct answer:

Explanation:

The easiest way to solve this equation is to work backwards. Start with the  for the third year and divide by  to get the second year's earning which were , then subtract  to get the first year which was .

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