5.4 Systems of Equations Applications

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 point(s) where the equations intersect.

Front

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

Back

A system of equations has no solution when the lines represented by the equations are parallel and never intersect.

Front

How do you find the cost of items using a system of equations?

Back

Set up equations based on the total cost and quantities of items, then solve the system to find the cost of each item.

Front

What is the slope-intercept form of a linear equation?

Back

Front

How do you calculate the slope from an equation in standard form?

Back

Front

What is the significance of the x-value in a system of equations?

Back

The x-value in a system of equations represents the horizontal coordinate of the intersection point of the equations.

Front

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

Back

Identify the variables, translate the relationships and totals into equations, and then form a system of equations.

Front

What is the graphical representation of a system of equations with one solution?

Back

The graphical representation shows two lines that intersect at exactly one point.

Front

What does it mean for a system of equations to be consistent?

Back

A consistent system of equations has at least one solution, meaning the lines intersect at one or more points.

Front

What does it mean for a system of equations to be inconsistent?

Back

An inconsistent system of equations has no solutions, meaning the lines are parallel and do not intersect.