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Algebra II : Equations

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Example Questions

Example Question #161 : Equations

Solve for and :

3x+5y=-9

2x-4y=16

Possible Answers:

x=-2

y=1

x=2

y=3

x=2

y=-3

x=1

y=1

Correct answer:

x=2

y=-3

Explanation:

There are two ways to solve this:

-The 1st equation can be mutliplied by while the 2nd equation can be multiplied by and added to the 1st equation to make it a single variable equation where

22y=-66

y=-3 .

This can be plugged into either equation to get x=2

-The 2nd equation can be simplified to,

x-2y=8

x=8+2y .

This value for can then be substituted into the first equation to make the equation single variable in y, 3(8+2y)+5y=-9 .

Solving, gives y=-3 , which can be plugged into either original equation to get x=2

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Example Question #162 : Equations

Solve f(-14) if $f(x)=-0.5x+\frac{42}{x}$ .

Possible Answers:

Correct answer:

Explanation:

Plug in for in the f(x) equation to get

$f(-14)=7+(\frac{42}{-14})=7-3=4$

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Example Question #32 : Solving Equations

Solve for f(x) . When x=2 .

f(x)=5x^3+2x-24

Possible Answers:

f(x)=-15

f(x)=20

f(x)=10

f(x)=14

f(x)=-20

Correct answer:

f(x)=20

Explanation:

Given the equation,

f(x)=5x^3+2x-24 and x=2

Plug in for to the equation, f(2)=5(2)^3+2(2)-24

Solve and simplify.

f(2)=5(8)+4-24

f(2)=40+4-24

f(2)=44-24

f(2)=20

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Example Question #81 : Functions And Lines

$f(x)=\frac{4x-2}{x+3}, x\neq-3$

Solve for f(x) , when x=0 .

Possible Answers:

$f(x)=\frac{1}{3}$

$f(x)=\frac{-2}{3}$

$f(x)=\frac{-1}{3}$

f(x)=0

$f(x)=\frac{2}{3}$

Correct answer:

$f(x)=\frac{-2}{3}$

Explanation:

$f(x)=\frac{4x-2}{x+3}, x\neq-3$

Plug in the value for .

$f(0)=\frac{4(0)-2}{(0)+3}$

Simplify

$f(0)=\frac{0-2}{3}$

Subtract

$f(0)=\frac{-2}{3}$

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Example Question #163 : Equations

x+y=32

and

$x=\frac{2}{3}y-2$

Solve for and .

Possible Answers:

$y=20\frac{2}{5},x=11\frac{3}{5}$

$y=20\frac{3}{5},x=11\frac{4}{5}$

$y=19\frac{2}{5},x=12\frac{3}{5}$

$y=11\frac{2}{5},x=20\frac{3}{5}$

None of the available answers

Correct answer:

$y=20\frac{2}{5},x=11\frac{3}{5}$

Explanation:

x+y=32 rearranges to

x=32-y

and

$x=\frac{2}{3}y-2$ , so

$32-y=\frac{2}{3}y-2$

$32-1\frac{2}{3}y=-2$

$-1\frac{2}{3}y=-34$

$-\frac{5}{3}y=-34$

$y=\frac{-34}{1}\cdot\frac{-3}{5}=\frac{102}{5}=20\frac{2}{5}$

$x=32-20\frac{2}{5}=11\frac{3}{5}$

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Example Question #1 : How To Find The Solution For A System Of Equations

Solve for (x, y) in the system of equations:

y = 3x + 4

2x + 3y = 34

Possible Answers:

(5, 19)

(4, 16)

(3, 13)

(2, 10)

The system has no solution

Correct answer:

(2, 10)

Explanation:

In the second equation, you can substitute 3x + 4 for from the first.

2x + 3y = 34

2x + 3 (3x + 4) = 34

2x + 3 (3x) + 3 (4) = 34

2x + 9x + 12 = 34

11x + 12 = 34

11x = 22

x = 2

Now, substitute 2 for in the first equation:

y = 3x + 4

y = 3 (2) + 4

y = 6 + 4

y = 10

The solution is (2, 10)

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Example Question #164 : Equations

Solve for :

ax-b=cd

Possible Answers:

$\frac{a}{cd+b}$

$\frac{cd+b}{a}$

$\frac{cd+a}{b}$

$\frac{b}{cd+a}$

None of the other answers

Correct answer:

$\frac{cd+b}{a}$

Explanation:

To solve for , you must isolate it from the other variables. Start by adding to both sides to give you ax=cd+b . Now, you need only to divide from both sides to completely isolate . This gives you a solution of $x=\frac{cd+b}{a}$ .

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Example Question #33 : Algebraic Functions

For the following equation, if x = 2, what is y?

y=x^3-4x+9

Possible Answers:

Correct answer:

Explanation:

On the equation, replace x with 2 and then simplify.

y=x^3-4x+9

y=(2)^3-4(2)+9

y=8-8+9

y=9

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Example Question #5 : How To Factor An Equation

Solve for $\small x$ .

x^2-5x-36

Possible Answers:

$x=-6,\ 4$

$x=-2,\ 5$

$x=-4,\ 9$

$x=2,\ 12$

$x=0,\ 3$

Correct answer:

$x=-4,\ 9$

Explanation:

x^2-5x-36

This is a quadratic equation. We can solve for $\small x$ either by factoring or using the quadratic formula. Since this equation is factorable, I will present the factoring method here.

The factored form of our equation should be in the format (A+B)(C+D)=0 .

To yield the first value in our original equation ( $\small x^2$ ), $\small A=x$ and $\small C=x$ .

(x+B)(x+D)=0

To yield the final term in our original equation ( $\small -36$ ), we can set $\small B=-9$ and $\small D=4$ .

$-9*4=-36\ \text{and}\ -9+4=-5$

(x-9)(x+4)=0

Now that the equation has been factored, we can evaluate $\small x$ . We set each factored term equal to zero and solve.

$\begin{matrix} x-9=0 &x+4=0 \\ x-9+9=0+9&x+4-4=0-4 \\ x=9 & x=-4 \end{matrix}$

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Example Question #35 : Solving Equations

Without drawing a graph of either equation, find the point where the two lines intersect.

Line 1 : y = 3x

Line 2 : y = x - 2

Possible Answers:

(2,0)

(-1,-3)

(1,3)

(0,-2)

(0,0)

Correct answer:

(-1,-3)

Explanation:

To find the point where these two lines intersect, set the equations equal to each other, such that is substituted with the side of the second equation. Solving this new equation for will give the -coordinate of the point of intersection.

3x = x - 2

Subtract from both sides.

(3x) - x = (x - 2) - x

2x = - 2

Divide both sides by 2.

$\frac{2x}{2} = \frac{-2}{2}$

x = - 1

Now substitute into either equation to find the -coordinate of the point of intersection.

y = 3x

y= 3(-1)

y = -3

With both coordinates, we know the point of intersection is (-1,-3) . One can plug in for and for in both equations to verify that this is correct.

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Algebra II : Equations

Study concepts, example questions & explanations for Algebra II

All Algebra II Resources

Example Questions

Example Question #161 : Equations

Example Question #162 : Equations

Example Question #32 : Solving Equations

Example Question #81 : Functions And Lines

Example Question #163 : Equations

Example Question #1 : How To Find The Solution For A System Of Equations

Example Question #164 : Equations

Example Question #33 : Algebraic Functions

Example Question #5 : How To Factor An Equation

Example Question #35 : Solving Equations

All Algebra II Resources

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