Systems of Equations: Substitution/Graphing

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 to solve a system of equations graphically?

Back

To solve a system of equations graphically means to plot the equations on a graph and identify the point(s) where they intersect, which represents the solution.

Front

What is the substitution method in solving systems of 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 systems of equations?

Back

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

Front

What is the solution to the system of equations: 2x + 3y = 6 and x - y = 1?

Back

The solution is (3, 0).

Front

How do you determine 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 have the same slope but different y-intercepts.

Front

How do you determine if a system of equations has infinitely many solutions?

Back

A system has infinitely many solutions if the equations represent the same line, meaning they have the same slope and y-intercept.

Front

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

Back

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

Front

What does it mean for two lines to be perpendicular?

Back

Two lines are perpendicular if the product of their slopes is -1.

Front

If y = 2x + 3, what is the y-intercept?

Back

The y-intercept is 3.