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Example Questions
Example Question #81 : Systems Of Equations
What is ?
Solve for by merging the equations so that gets factored out. To do so, multiply the lower equation by (so that at the top is subtracted by )
Example Question #221 : New Sat
If , then
,
Example Question #43 : New Sat Math No Calculator
Expand the following expression found below:
If a problem asks you to expand an expression, you must use the Distributive property. If you are using the FOIL method, you first multiply the first term in each parentheses by each other, followed by the outside terms, then the inside terms, and then the last terms. This is illustrated below.
First, you multiply which equals
Second, you multiply
Third, you multiply
Last, you multiply
Then you simply rearrange them in order of exponents to get
Example Question #3 : Rational Expressions
If , then which of the following must be also true?
Example Question #45 : New Sat Math No Calculator
What is the value of the -intercept for the line given below?
The x-intercept is where the line crosses the x-axis. In other words,
This gives:
Subtracting 98 from both sides gives:
Dividing both sides by 14 gives the final answer:
Example Question #31 : Coordinate Geometry
Which of the following lines is parallel to:
First write the equation in slope intercept form. Add to both sides to get . Now divide both sides by to get . The slope of this line is , so any line that also has a slope of would be parallel to it. The correct answer is .
Example Question #46 : New Sat Math No Calculator
Find the extraneous solution for
There are no extraneous solutions
Now lets plug these values into our original equation.
For
So this isn't an extraneous solution.
For
Since , is an extraneous solution.
Example Question #222 : New Sat
Solve
First multiply by the denominator on each side
Expand left side, and solve for
Example Question #48 : New Sat Math No Calculator
Given:
How many solutions will there be for the system of equations?
Use the substitution method to solve the system of equations. There are two ways to do this - either substitute the first equation into the second, or the second equation into the first. Since the second equation is already solved for one variable, we will choose the latter.
Now factor the equation:
or
For this particular question, you could stop right here, as you can only need to know the number of solutions not the ordered pair of the solutions. Here there are two solutions. The ordered pairs would be:
and
Example Question #49 : New Sat Math No Calculator
Bob and Jill go eat dinner at a fancy restaurant. Bob gets lobster and Jill gets crab legs. The lobster cost , and the crab legs cost . If they leave tip, how much is the combined bill?
To do this, we need to sum up each meal, and then convert the tip into a decimal.
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