# ACT Math: Algebra

## SAT Question of the Day

The SAT question of the day is an Identifying Sentence Errors question that has already been addressed on this blog: click here to see an explanation.

## ACT Question of the Day

The ACT question of the day is a math question that tests your knowledge of algebra.

The question starts out by giving you two different equations: x + 2y = 1 and 2x + y = 5.  The bottom line, the question that you must answer is x + y = ?

When you have two distinct equations, you have two different ways that you can solve the problem: substitution and elimination.  Substitution is best to use when one equation has only one variable.  Elimination is best to use when solving for one variable would be messy.  Take a look at the first equation: x + 2y = 1.  It would be very simple to solve this for x!  You may be able to save a few seconds by using substitution.  You certainly want to use the most efficient method on each problem in a timed test, but for this problem it is most important to attack it without spending too much time thinking about which method to choose!  Let's start with substitution.  Solve the first equation for x.

x + 2y = 1

x = 1 - 2y

Now that you have solved for x, substitute the answer that you found into the other equation wherever you see an x.

2x + y = 5

2(1 - 2y) + y = 5

2 - 4y + y = 5

2 - 3y = 5

-3y = 3

y = -1

You now know that y = -1.  Plug that back into the answer that you found for x so that you get a numerical value for x.

x = 1 - 2y

x = 1 - 2(-1)

x = 1 + 2

x = 3                 There is still one more step!

Your problem asked you to find x + y.  Add the two values together:

x + y =

3 + (-1) = 2         <--- Here is your final answer!

The correct answer is (G).

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Note: you can also get the correct answer quickly by using elimination.  Here is an explanation of this method.

Set up your equation by writing one equation above the other.  When you do this, you will notice that you can easily cancel out the x if you multiply everything in the first equation by 2:

(x + 2y = 1)     --->     2(x + 2y = 1)    --->    (2x + 4y = 2)

- (2x + y = 5)     --->    - (2x + y = 5)    --->  - (2x +  y  =  5)

3y = -3

y = -1

Now that you know y = -1, plug it back into the easiest of your original equations:

x + 2y = 1

x + 2(-1) = 1

x - 2 = 1

x = 3

You still aren't finished because you need to add x and y to get your final answer:

x + y =

3 + (-1) = 2   <---  This is your final answer.

The correct answer is (G).

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