Systems of Equations Review

Front

What is a system of equations?

Back

A system of equations is a set of two or more equations with the same variables that are solved simultaneously.

Front

How can you determine if a point is a solution to a system of equations?

Back

A point (x,y) is a solution if it satisfies all equations in the system.

Front

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

Back

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

Front

What is the substitution method in solving systems of equations?

Back

The substitution method involves solving one equation for one variable and 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 other.

Front

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

Back

It means the lines represented by the equations are parallel and never intersect.

Front

What is the graphical interpretation of a system of equations?

Back

The solutions to the system are the points where the graphs of the equations intersect.

Front

How do you solve a system of equations using graphing?

Back

You graph each equation on the same coordinate plane and identify the point(s) of intersection.

Front

What is the first step in solving the system: 3x + 3y = 3 and y = 3x + 5?

Back

The first step is to substitute y from the second equation into the first equation.

Front

What is the solution to the system of equations: -x + 9y = -5 and x - 5y = 1?

Back

The solution is (-4, -1).