Unit Test 3A (25%)

Front

What is a system of linear equations?

Back

A system of linear equations is a set of two or more linear equations with the same variables. The solution is the point(s) where the equations intersect on a graph.

Front

How do you solve a system of equations by elimination?

Back

To solve by elimination, you manipulate the equations to eliminate one variable, allowing you to solve for the other variable. Then substitute back to find the first variable.

Front

What does it mean if a system of equations has no solution?

Back

A system has no solution if the lines represented by the equations are parallel, meaning they never intersect.

Front

What does it mean if a system of equations has infinitely many solutions?

Back

A system has infinitely many solutions if the equations represent the same line, meaning every point on the line is a solution.

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 they represent the same scenario.

Front

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

Back

The slope-intercept form is y = mx + b, where m is the slope and b is the y-intercept.

Front

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

Back

Set up equations based on the total cost and quantities purchased, then solve the system to find the cost per item.

Front

What is the significance of the coefficients in a linear equation?

Back

The coefficients represent the rate of change of the dependent variable with respect to the independent variable.

Front

What is the graphical representation of a linear equation?

Back

A linear equation is represented graphically as a straight line on a coordinate plane.

Front

What is the first step in solving a system of equations by graphing?

Back

The first step is to rearrange each equation into slope-intercept form (y = mx + b) to easily plot them on a graph.