$$\left(x^5y^2\right)\ \left(x^2y^3\right)\ =\ $$

$$x^{7\ }y^5\ $$ When multiplying variable with exponents you add the exponents of the like variables

$$\left(a^3b^4\right)\ \left(a^2b\right)\ =\ $$

$$a^{5\ }b^5\ $$ When multiplying variables with exponents, add the exponents of the like variables

What does it mean when two lines in a system of equations coincide?

They represent the same line, leading to infinite solutions

How can you verify the solution of a system of equations?

Substitute the solution back into the original equations to check if they hold true

How can you verify the solution of a system of equations?

Substitute the solution back into the original equations to check if they hold true

$$\left(a^5\right)^3$$

$$a^{15}$$ When raising an exponent by and exponent you multiply the exponents

$$\left(b^4\right)^2$$

$$b^{8}$$ When raising a power to another power, multiply the exponents

$$2\ \left(x^3y^5\right)^3$$

$$2x^{9\ \ }y^{15}$$ The 2 in front is not raised by 3, but only what is in parenthesis. You multiply the exponents when raising on exponent by another.

$$3\ \left(a^2b^4\right)^2$$

$$3a^{4\ \ }b^{8}$$ The 3 in front is not raised by 2, but only what is in parenthesis. You multiply the exponents when raising one exponent by another.

$$\ \frac{x^5y^6}{xy^2}\ =$$

$$x^{4\ }y^4$$ When you are dividing you subtract the smallest exponents of like variables. The variable remains where the position where it is greatest. In this case both variables exponents are greater in the numerator so they remain in the numerator.

$$\ \frac{a^7b^3}{a^2b}\ =$$

$$a^{5\ }b^2$$ When dividing, subtract the exponents of like variables. The variable stays in the position where its exponent is larger. Here, both variables have larger exponents in the numerator, so they remain there.

1, any number or variable raised to the 0 power is 1.

$$2a^{0\ }\ +\ 5\ =\ $$

7, anything raised to the power of is 1. 2 x 1 + 5 = 7

$$2x\ +\ 5\ +\ 5x\ =\ $$

7x + 5, Combine like terms, when you can only combine like variable with the same exponent. You add the coefficients of the like variables and keep the variable as is.

$$3y\ +\ 4\ +\ 2y\ =\ $$

5y + 4, Combine like terms by adding the coefficients of the same variable. Keep the variable unchanged.

$$3y\ +\ 4\ \ -\ y\ +\ 2y^{2\ \ \ \ }$$ Simplify and put in Standard Form.

$$\ 2y^{2\ \ \ \ }+\ 2y\ +\ 4$$ Combine like terms by adding the coefficients of the same variable. Keep the variable unchanged.

System of Equations Flashcards

Student preview

23 questions

Show all answers

1.

FLASHCARD QUESTION

Front

What is the solution to Parallel lines in a system of equations

Back

No solution

2.

FLASHCARD QUESTION

Front

What is the solution to Intersecting lines in a system of equations

Back

One solution, it is the point where they interesect

3.

FLASHCARD QUESTION

Front

What is the solution to Single line in a system of equations

Back

Infinite solutions

4.

FLASHCARD QUESTION

Front

Methods to solve a system of equations

Back

Elimination, substitution, graphing

5.

FLASHCARD QUESTION

Front

Back

6.

FLASHCARD QUESTION

Front

Back

7.

FLASHCARD QUESTION

Front

What is the graphical representation of a system with no solution?

Back

Parallel lines that never intersect

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