2nd Semester Algebra Review

What is the solution of the system found from the graph below?

• $\left(1,1\right)$

• $\left(-4,1\right)$

• $\left(1,-4\right)$

• $\left(-1,-4\right)$

For the above graph, check all statements that are true. (more than one can apply)

• The lines are parallel

• The system has infinitely many solutions.

• The system has no solutions.

• the solution to the system is (0, 0)

For the given system, check all the steps used to solve the system. (more than one answer may apply) 

Reminder that you may solve the problem with different steps, but that does not mean the ones listed do no apply.

•  $3x-2=-7x+18$  

•  $10x-2=18$  

•  $10x=20$  

•  $x=2$  

•  $y=-7\left(2\right)+18$  

When solving the sytem:

 $y=-2x-8$  

 $2x+5y=-16$  
The first step is given, what is the best answer for the next step according to notes the class.
 $2x+5\left(-2x-8\right)=-16$  

•  $2x-10x-40=-16$  

•  $x=-3$  

•  $y=-2$  

•  $y=-2\cdot-3-8$  

In the given system, when solving by Elimination Method, what is a good explanation of the first step in eliminating one of the variables according to our notes and examples from class?
 $18x-5y=-25$  
 $-9x-3y=-15$  

• Eliminate one variable by adding the equations.

• Eliminate one variable by subtracting the equations.

• Multiply the 2nd equation by 2, in order to get opposites.

• Solve the equation

When simplifying the expression  $\left(7x^3\right)\cdot\left(6x^5\right)$  , what is the best explanation for combining the exponents?

• Remove parentheses

• When multiplying expressions, add the exponents.

• When multiplying, multiply the exponents.

• Calculate the product

When simplifying the expression  $\left(\frac{2x}{3y^2}\right)^3$  , check all of the exponent rules that apply to simplifying the problem.

•  $a^0=1$  

•  $\left(a^m\right)^n=a^{mn}$  

•  $\left(\frac{a}{b}\right)^m=\frac{a^m}{b^n}$  

•  $\frac{a^m}{a^n}=a^{m-n}$  

Check the two expressions that multiply together to get the result  $36xy^6$  

•  $9x^3y^2$  

•  $4x^{-1}y^3$  

•  $4x^{-2}y^4$  

•  $9xy^3$  

In the problem $\left(3x\right)^3=9x^3$ , the answer is wrong. What is the BEST explanation of the mistake the student made to get the wrong answer?

• The answer, is in fact, correct.

• They did not use the properties of exponents correctly.

• They multiplied the 3 and 3 instead of taking 3 to the 3 power.

• They added the exponent when they should have multiplied them.

True or False? When simplifying the expression  $\frac{x^{10}}{x^5}$  , you divide the exponents.