[a] U5D2 Writing Systems

Front

What is a system of equations?

Back

A system of equations is a set of two or more equations with the same variables. The solution to the system is the set of values that satisfy all equations simultaneously.

Front

How do you represent the total number of coins in a system of equations?

Back

You can represent the total number of coins by using an equation where the sum of the variables equals the total number of coins, e.g., x + y = total number of coins.

Front

What is the value of a dime in dollars?

Back

A dime is worth $0.10.

Front

What is the value of a quarter in dollars?

Back

A quarter is worth $0.25.

Front

How do you set up an equation for the total value of coins?

Back

You set up an equation by multiplying the number of each type of coin by its value and summing these products to equal the total value, e.g., 0.10x + 0.25y = total value.

Front

What does the variable 'x' typically represent in coin problems?

Back

In coin problems, 'x' typically represents the number of one type of coin, such as dimes or nickels.

Front

What does the variable 'y' typically represent in coin problems?

Back

In coin problems, 'y' typically represents the number of another type of coin, such as quarters or dimes.

Front

How can you solve a system of equations graphically?

Back

You can solve a system of equations graphically by plotting each equation on a graph and finding the point(s) where the lines intersect, which represents the solution.

Front

What is substitution in the context of solving systems of equations?

Back

Substitution is a method where you solve one equation for one variable and then substitute that expression into the other equation to find the values of the variables.

Front

What is elimination in the context of solving systems of equations?

Back

Elimination is a method where you add or subtract equations to eliminate one variable, making it easier to solve for the remaining variable.