Algebra 1 : Linear Equations
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Example Questions
Example Question #11 : How To Write Expressions And Equations
Solve by substitution method:
From the second equation and by solving for 
Replacing 
we get
Solving for 
Replacing 
Hence the solution to the above system of linear equations is 
Example Question #12 : How To Write Expressions And Equations
Solve the following system of linear equations by the elimination method:
We would like to eliminate 
Hence we multiply the first equation by 
Adding the above two equations eliminates the variable 
and so
Replacing 
solving for 
Hence the solution is 
Example Question #931 : Algebra 1
For the following two linear equations determine whether the two lines are __________:
(1) parallel
(2) perpendicular
(3) neither
(4) dependent
Parallel
Dependent
Neither
None of the above
Perpendicular
Dependent
These two equations represent the same line and they "cross' at infinitely many points. Therefore these systems are dependent.
Example Question #12 : How To Write Expressions And Equations
Example Question #932 : Algebra 1
Which of the following sentences translates to the algebraic equation 
Eight multiplied by the difference of three and a number is equal to forty.
The product of three and a number less eight is equal to forty.
Eight multiplied by the difference of a number and three is equal to forty.
The product of eight and a number subtracted from three is equal to forty.
Three subtracted from the product of eight and a number is equal to forty.
Eight multiplied by the difference of a number and three is equal to forty.
The expression on the left shows eight being multiplied by an expression in parentheses; that expression is the difference of an unknown number and three. The whole right expression is therefore worded as "Eight multiplied by the difference of a number and three"; the equality symbol and the forty round out the answer.
Example Question #933 : Algebra 1
Which of the following sentences translates to the equation 
Five divided into the difference of a number and nine is equal to eighty.
Five subtracted from the quotient of a number and nine is equal to eighty.
Nine subtracted from the quotient of a number and five is equal to eighty.
Nine divided by the difference of a number and five is equal to eighty.
Five divided by the difference of a number and nine is equal to eighty.
Five divided into the difference of a number and nine is equal to eighty.
Example Question #934 : Algebra 1
In a room full of 60 people, 32 are women and 20 have blonde hair. Of the men, 16 do not have blonde hair. How many blonde women are in the room?
First, calculate the total number of men.
Next, calculate the number of blonde men.
Now we can calculate the number of blonde women.
Example Question #22 : How To Write Expressions And Equations
A train travels for 2.5 hours at 60mph. For the next hour, the train travels at 40mph. How far does the train travel over the course of 3.5 hours?
Use the distance equation, where 
The first rate is 60mph, and the first time is 2.5 hours. The second rate is 40mph, and the second time is 1 hour.
Example Question #23 : How To Write Expressions And Equations
The sum of two numbers is forty, and one number is three less than twice the other number.
Write an equation that represents this sentence.
Suppose one number is 
The other number is "three less than twice the other number." Twice our other number is 
We are told that the sum of these two numbers is forty.
Now we can simplify.
Example Question #24 : How To Write Expressions And Equations
Represent this number in scientific notation:
Write this number with the decimal point after it.
Move the decimal point to the position after the first nonzero digit, which here is the 1. Note that the resulting number, after truncating the trailing zeroes, is
Also note that the number of places the decimal point moved is 23. Since the point was moved left the exponent will be 23, and the correct choice is
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