4-7: Writing Systems of Linear Equations

Front

What is a linear equation?

Back

Front

What does the slope of a line represent?

Back

The slope of a line represents the rate of change of the y-value with respect to the x-value. It indicates how steep the line is.

Front

What is the y-intercept of a linear equation?

Back

Front

How can you determine if two lines are parallel?

Back

Two lines are parallel if they have the same slope but different y-intercepts.

Front

What does it mean for two lines to be perpendicular?

Back

Two lines are perpendicular if the product of their slopes is -1. This means that one line has a slope that is the negative reciprocal of the other.

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.

Front

How can you solve a system of equations graphically?

Back

To solve a system of equations graphically, plot both equations on the same graph and identify the point(s) where they intersect.

Front

What is substitution in solving systems of equations?

Back

Substitution is a method where you solve one equation for one variable and then substitute that expression into the other equation.

Front

What is elimination in solving systems of equations?

Back

Elimination is a method where you add or subtract equations to eliminate one variable, making it easier to solve for the other.

Front

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

Back

If a system of equations has no solution, it means the lines are parallel and never intersect.