ALGEBRA Full Explanation

This is the link that you can use for all essential algebraic expressions and explanations. From substitution to linear equations, you can use this resource to solve algebra equations step-by-step.

 

how to solve algebra equations

 

 

S.O.E. and Inequalities and adding, subtracting, multiplying and dividing monomials

System of Equations

x  |  y=4x -1 | y |  (x, y)  |

-3    4(-3) -1     -11    (3, -11)

-2    4(-2) -1    -9    (-2, -9)

-1    4(-1) -1     -5     (-1. -5)

0     4 (0) -1     -1    (0. -3)

1     4 (1) -1       3     (1, 1)

2    4 (2) -1       7     (2, 7)

3    4 (3) -1       11    (3, 11)

 

x  |  y=-x +4|   y |  (x, y)  |

-3    -(-3) +4  7     (-3, 7)

-2    -(-2) +4  6    (-2, 6)

-1    -(-1) +4   5     (-1. -5)

0     -(0) +4   4    (0. -3)

1     -(1) +4     3     (1, 1)

2    -(2) -1       2    (2, 7)

3    -(3) -1       1    (3, 11)

 

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VOCABULARY

The two lines intersect at the solution. The solution is also where the two lines overlap. Always mark the solution area with a bold S.

A system of inequalities is a two inequalities presented as a set.

To solute or not solute

Determine if coordinate (1,4) is a solution for the systems below

y=x+3            y=2x-2

4=1+3            4=2(1)-2

4=4                 4=0

CHECK           DOES NOT CHECK

The solution is not a solution for this system of equations

y=5x -1        y=-2x + 6

4=5(1)-1      4= -2(1)+6

4=4                4=4

CHECK          CHECK

The solution is a solution for this system of equations

Problem:

y=5x-1
y=-2x+6

GRAPHING SYSTEMS OF EQUATIONS

y=-3x+2
y=3x-4

solution (1, -1)

There are two ways to graph a system of equations. If the equations are presented

in y-intercept form, then you would plot your first point at the y-intercept. Then,

you would use the slope (mx) to plot your remaining points. The solution will always be the location in which the two lines intersect.

Secondly, you can use the substitution method to find your x and y value for each equation. To prove that your solution is correct, graph each of the lines by placing them in y-intercept form. If the solution that you receive after you create your graph is the same as the solution you developed with using the substitution method, then your answer is correct.

ex.     x + y = 4

2x  – y = 5

Step 1: put the first equation into y-intercept form (y = -x + 4)

Step 2: substitute the new equation into the second-given equation (2x – (-x + 4) = 5)

Step 3: combine like terms (2x + x + 4 =5) –> (3x + 4 = 5) —> (3x – 4+4 = 5+4) —>

(3x/3 = 9/3) —>x = 3

Step 4: substitute the new equation into the first-given equation (3+ y = 4)

Step 5: subtract 1/3 from both sides of the equation (3-3 + y = 4 -3)

Step 6: solve (y = 4 – 3) —> y = 1

Step 7: write your solution ( 3, 1)

Step 8: make a graph to check your solution ( 3+1=4 ), ( 2(3) – 1 = 5) CHECK!

ALGEBRA FOUR

Image via Wikipedia

Similar to the game Connect Four,  the winner of an Algebra 4 game has successfully connected four pieces horizontally, vertically, or diagonally. In order to place a piece in a column, a player must correctly solve an equation involving variables, one-step or two steps, and polynomials.