Ch. 8 Test: Systems of Linear Equations

Front

What is a system of linear equations?

Back

A set of two or more linear equations with the same variables.

Front

What does it mean to solve a system of equations by elimination?

Back

It means to eliminate one variable by adding or subtracting the equations, making it easier to solve for the other variable.

Front

What is the graphical representation of a system of equations with no solution?

Back

The lines representing the equations are parallel and never intersect.

Front

What does it mean if two equations represent the same line?

Back

It means there are infinite solutions, as every point on the line is a solution.

Front

How do you determine if a system of equations has one solution?

Back

If the lines intersect at exactly one point, the system has one solution.

Front

What is the substitution method in solving systems of equations?

Back

It involves solving one equation for one variable and substituting that expression into the other equation.

Front

What does the x represent in the equation y = mx + b?

Back

The x represents the independent variable, often the input value in a function.

Front

What is the slope of a line?

Back

The slope is the ratio of the rise (change in y) over the run (change in x) between two points on the line.

Front

How can you tell if a system of equations is consistent?

Back

A system is consistent if it has at least one solution.

Front

What is the meaning of the y-intercept in a linear equation?

Back

The y-intercept is the point where the line crosses the y-axis, representing the value of y when x is 0.