Algebra Flashcards
What is an equation?
It is a complete sentence that has a subject, a verb, and an object: subject equals object, i.e., one expression equals to another expression.
2x - z = y + 4
Two x minus z equals y plus four
Is it possible to simplify or evaluate expressions that are part of equations?
Yes. All the rules about simplifying or evaluating expressions appliers in the world of equations, because equations are made up of expressions.
You can simplify or evaluate an expression on just one side of an equation, because you are not changing the value of that expression.
Is it possible to change the value of one side of the equation?
Yes, as long as you do the same thing to both sides of the equation:
x + 5 = 8
x + 5 - 5 = 8 - 5
x = 3
a + b = 5d
(a + b) / 5 = 5d / 5
(a + b) / 5 = d
How to isolate a variable in complicated expressions?
You need to do PEMDAS in the reverse order.
So first, send the additions and subtractions to the other side of the equation.
Then send the multiplication and division to the other side.
Next send roots or exponents to the other side.
Finally eliminate/drop the parenthesis as they are left over and send the operations previously within the parenthesis to the other side of the equation.
What to do if you have a variable in multiple places in an equation?
Combine like terms, which might be on different sides of the equation
What to do if you have a variable in a denominator?
Multiply both sides of the equation to get the variable out of the denominator
What to do if you have a variable in the exponent?
Rewrite the bases in a way that the bases are equal.
3^x = 27^4
3^x = (3^3)^4
3^x = 3^12
x = 12
This rule is only not true if the base is 1, 0, or -1
What is a system of equations?
Is a group of more than one equation. Solving a system of two equations with two variables, for example, x and y, means finding values for x and y that make both equations true at the same time.
How to solve a system of equations by isolating and then substituting?
Isolate one variable in one of the equations. Next, substitute into the other equation.
If the problem asks for the value of “x”, first isolate “y”, it will save time.
Isolate the variable in whichever equation you think is easier to deal with:
(a) 2x - 3y = 16
(b) y - x = - 7
y = x - 7
2x - 3(x - 7) = 16
2x - 3x + 21 = 16
-x + 21 = 16
- x = - 5
x = 5
How to solve a system of equation for an Unknown?
You can add or subtract the equations, by putting the expression before the equal sign in your left and he expression after the equal sign in your right
Addition:
a + b = 11
a - b = 5
————–
2a = 16
a = 8
Subtraction:
5n + m = 17
2n + m = 11
—————–
3n = 6
n = 2
