1) Isolate variable on one side of the equation2) Move all constants over to the other side of the equation
4) If there is a constant in front of the variable, divide each side of the equation by this constant to remove itElimination Method - The goal is to remove one variable by subtracting one equation from the other
ax + by = c
dx + ey = f
We need to find a number (n) to multiply top and bottom equations by such that na = nd or nb = ne so that we can eliminate the x terms or y terms
Substitution Method - Substitute one equation into the other
Rearrange Equation dx + ey = f, we get
| x = | f - ey |
| d |
We then substitute that into Equation 1 where we see the variable x
Cramers Rule - Learn the 3 shortcut equations
Δ = a * e - b * d
Variable 1 Numerator = c * e - b * f
Variable 2 Numerator = a * f - c * d
| Variable 1 = | Variable 1 Numerator |
| Δ |
| Variable 2 = | Variable 2 Numerator |
| Δ |
Given 2 points (x1,y1) and (x2,y2), the slope of the line (m) is:
| m = | y2 - y1 |
| x2 - x1 |
The line equation is y = mx + b * 2 lines are parallel if their slopes equal each other
* 2 lines are perpendicular if their slopes are negative reciprocals of each other, i.e., m and -1/m.
* 2 lines are just intersecting if both conditions above fail.(a + b)(c + d) is expanded using First-Outside-Inside-Last (FOIL)
ac + ad + bc + bdax2 + bx + c = 0
When a = 1, you solve these by finding two numbers that x and y such that x + y = b and xy = cab/c = (c√a)b is solved by doing the following
Take the cth root of b. Then, take that value, and raise it to the power of b
272/3 = 3√27 = 3 --> 32 = 9i = √-1
i2= -1
i3= -i
i4= 1
They key is to find the maximum power you can of 4 since i4 = 1ax2 - by2 = (ax + by)(ax - by)Sum of Cubes: a3 + b3 = (a + b)(a2 - ab + b2)
Difference of Cubes: a3 - b3 = (a - b)(a2 + ab + b2)
If there is not a shortcut formula, you first factor any constants that you can. Next, you go through each variable in the expression. If every term contains a variable, that variable can be factored out using the lowest power that you see in that expression, else, it cannot be factored.
Factoring Rational Expressions:
| x2 + 6x + 8 | |
| x2 + 9x + 20 |
Factor the top and bottom to get this answer
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