6.4 Review

Front

What is a linear system?

Back

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

Front

How do you represent the sum of two numbers algebraically?

Back

If x and y are the two numbers, their sum can be represented as x + y = S, where S is the total sum.

Front

What does it mean for one number to be '4 less than triple another number'?

Back

If y is the other number, then the first number can be expressed as x = 3y - 4.

Front

How do you set up a linear equation for a total value problem?

Back

Identify the variables, write an equation that represents the total value, and ensure the equation reflects the relationship between the variables.

Front

What is the formula to find the difference between two numbers?

Back

If x and y are the two numbers, their difference can be represented as x - y = D, where D is the difference.

Front

How do you express the total number of items in a system?

Back

If a and b are the two types of items, the total can be expressed as a + b = T, where T is the total number of items.

Front

What is the significance of coefficients in a linear equation?

Back

Coefficients represent the number of units of each variable in the equation. They determine how much each variable contributes to the total.

Front

How do you solve a linear system using substitution?

Back

1. Solve one equation for one variable. 2. Substitute that expression into the other equation. 3. Solve for the remaining variable.

Front

What is the graphical representation of a linear equation?

Back

A linear equation can be represented graphically as a straight line on a coordinate plane, where the x-axis and y-axis represent the variables.

Front

What does it mean for two equations to be consistent?

Back

Two equations are consistent if they have at least one solution in common, meaning they intersect at one or more points on a graph.