Algebra II web site

Greg's Algebra II Page

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Solving Linear Equations

All linear equations are easy because they are always in the same form. They always one y, one x, one m, and one b. Solving them is just getting the right variable by itself.

Problem Solved	Comments
Solve 3x + 17 = 4x -3	You start getting the variables and the constants on opposite sides of the equal sign. To do this you add a +3 to both sides and Subtract 3x to both sides. You add +3 to both sides to keep them equal. This is the same reason for subtracting on both sides.
17 + 3 = 4x - 3x	By adding or subtracting the selcted numbers you get this. Now all you have to do is simplify the equation for a solution.
20 = x	In simplifying the problem you are able to get your answer.

Now Let's try a more difficult problem!

Solve (5/3)n -17 = 24n + 13 Again start by getting the variables and constants on both sides. Add +17 and subtract 24n to both sides.

(5/3)n - 24n = 17 + 13 Simplify the equation by adding like numbers.

(77/3)n = 30 Now all you have to do is solve for n. In this situation you need to multiply the number preceding the variable by its recipricol. This is done to make it equal to 1 and 1n is the same thing as n. In this problem you need to multiply both side by (3/77).

n = 90/77 N is equal to 90/77. It is best to keep this number as a fraction for graphing purposes.

Next is Solving Literal Equations

All literal equations are the same thing as linear equtions only they have more than one variable which doesn't allow you to solve for an exact value.

Solve M = FD for D This equation for Mass (M) is solved just as simply as the linear equation. In solving for D all you have to do is divide both sides by F.

(M / F) = D Here is your solution.

Now let's try a more difficult one!

Solve A = (Vf -Vi) / T for Vf This formula solves for acceleration (A). Get rid of the denominator and multiply both sides by T.

AT = Vf - Vi To finish this easy problem all you have to do is add Vi to both sides.

AT + Vi = Vf This is your solution.

Writing Equations

Equations can be written in 3 different forms. Standard, Slope-Intercept, and Point-Slope forms.

Let's start with Point-Slope form

(9,15) Slope = 7/3 In Point-Slope form you are given a point on the line along with the lines slope.

y - y₁= m(x - x₁) Point-Slope form is written in an equation and after you get the information all you have to do is fill it in.

y - 15 = 7/3 ( x - 9 ) In this equation you fill in 7/3 in m because m is the symbol foor slope. The rest is academic and you have Point-Slope form.

Now let's convert this into Slope-Intercept form.

y = 7/3 ( x - 9 ) +15 Distribute out the 7/3 to the numbers in the parenthesis.

y = 7/3x -21 + 15 Add +15.

y = 7/3x - 6 This is Slope-Intercept form. The 7/3 is the slope and the -6 the y-intercept.

Now a few more steps and we will be in Standard form.

9y = 21x - 54 Multiply all the numbers by the same values so they all are whole numbers. Now you can subtrac 21x from both sides.

-21x + 9y = -54 This is standard form except for a minor rule that is implemented now. Never lead a standard form equation with a negative number. In this situation all you do is change the signs of all the values.

21x + -9y = 54 This is your solution.

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Solve (5/3)n -17 = 24n + 13	Again start by getting the variables and constants on both sides. Add +17 and subtract 24n to both sides.
(5/3)n - 24n = 17 + 13	Simplify the equation by adding like numbers.
(77/3)n = 30	Now all you have to do is solve for n. In this situation you need to multiply the number preceding the variable by its recipricol. This is done to make it equal to 1 and 1n is the same thing as n. In this problem you need to multiply both side by (3/77).
n = 90/77	N is equal to 90/77. It is best to keep this number as a fraction for graphing purposes.

Solve M = FD for D	This equation for Mass (M) is solved just as simply as the linear equation. In solving for D all you have to do is divide both sides by F.
(M / F) = D	Here is your solution.

Solve A = (Vf -Vi) / T for Vf	This formula solves for acceleration (A). Get rid of the denominator and multiply both sides by T.
AT = Vf - Vi	To finish this easy problem all you have to do is add Vi to both sides.
AT + Vi = Vf	This is your solution.

(9,15) Slope = 7/3	In Point-Slope form you are given a point on the line along with the lines slope.
y - y₁= m(x - x₁)	Point-Slope form is written in an equation and after you get the information all you have to do is fill it in.
y - 15 = 7/3 ( x - 9 )	In this equation you fill in 7/3 in m because m is the symbol foor slope. The rest is academic and you have Point-Slope form.

y = 7/3 ( x - 9 ) +15	Distribute out the 7/3 to the numbers in the parenthesis.
y = 7/3x -21 + 15	Add +15.
y = 7/3x - 6	This is Slope-Intercept form. The 7/3 is the slope and the -6 the y-intercept.

9y = 21x - 54	Multiply all the numbers by the same values so they all are whole numbers. Now you can subtrac 21x from both sides.
-21x + 9y = -54	This is standard form except for a minor rule that is implemented now. Never lead a standard form equation with a negative number. In this situation all you do is change the signs of all the values.
21x + -9y = 54	This is your solution.