solving linear equations graphically and algebraically

Front

What is a linear equation?

Back

A linear equation is an equation that makes a straight line when graphed. It can be written in the form y = mx + b, where m is the slope and b is the y-intercept.

Front

What does the slope of a line represent?

Back

The slope of a line represents the rate of change of y with respect to x. It indicates how steep the line is and the direction it goes (positive or negative).

Front

What is the y-intercept of a linear equation?

Back

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

Front

How do you find the x-intercept of a linear equation?

Back

To find the x-intercept, set y = 0 in the equation and solve for x.

Front

What does it mean for two lines to be parallel?

Back

Two lines are parallel if they have the same slope but different y-intercepts, meaning they will never intersect.

Front

What does it mean for two lines to be coincident?

Back

Two lines are coincident if they lie on top of each other, meaning they have the same slope and y-intercept, resulting in infinitely many solutions.

Front

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

Back

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

Front

How do you solve a system of linear equations graphically?

Back

To solve graphically, plot both equations on the same graph and identify the point(s) where they intersect. This point(s) represents the solution(s).

Front

What is the substitution method in solving linear equations?

Back

The substitution method involves solving one equation for one variable and then substituting that expression into the other equation.

Front

What is the elimination method in solving linear equations?

Back

The elimination method involves adding or subtracting equations to eliminate one variable, making it easier to solve for the other variable.