Systems Review

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 is the set of values that satisfy all equations in the system.

Front

How do you represent a word problem as a system of equations?

Back

Identify the variables, translate the relationships and conditions into equations, and ensure the equations reflect the problem's constraints.

Front

What does it mean for a system of equations to have no solution?

Back

A system has no solution when the equations represent parallel lines that never intersect.

Front

What does it mean for a system of equations to have one solution?

Back

A system has one solution when the equations represent lines that intersect at exactly one point.

Front

What does it mean for a system of equations to have infinite solutions?

Back

A system has infinite solutions when the equations represent the same line, meaning every point on the line is a solution.

Front

How do you find the solution to a system of equations graphically?

Back

Plot the equations on a graph and identify the point(s) where the lines intersect.

Front

What is the perimeter of a rectangle?

Back

The perimeter of a rectangle is the total distance around it, calculated as P = 2l + 2w, where l is the length and w is the width.

Front

How do you express the width of a rectangle in terms of its length?

Back

If the width is nine meters less than twice the length, it can be expressed as w = 2l - 9.

Front

What is the relationship between the number of coins and their total value?

Back

The total value of coins can be expressed as an equation where the value of each type of coin is multiplied by the number of coins.

Front

How do you set up a system of equations for a word problem involving coins?

Back

Define variables for each type of coin, create an equation for the total number of coins, and another for the total value.