Solving Systems of Equations

Front

What is a system of equations?

Back

A set of two or more equations with the same variables that are solved together.

Front

What does it mean for two equations to intersect on a graph?

Back

It means that the solution to the system of equations is the point where the two lines meet, representing the values of the variables that satisfy both equations.

Front

What is the substitution method in solving systems of equations?

Back

A method where one equation is solved for one variable, and that expression is substituted into the other equation.

Front

What is the elimination method in solving systems of equations?

Back

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

Front

How do you determine if a system of equations has no solution?

Back

If the equations represent parallel lines, they will never intersect, indicating no solution.

Front

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

Back

If the equations represent the same line, every point on that line is a solution, indicating infinitely many solutions.

Front

What is the graphical representation of a system of equations?

Back

It is represented by the lines of the equations plotted on a coordinate plane.

Front

What is the first step in solving a system of equations using substitution?

Back

Solve one of the equations for one variable in terms of the other variable.

Front

What is the first step in solving a system of equations using elimination?

Back

Align the equations and manipulate them to eliminate one variable by addition or subtraction.

Front

Solve for x and y: 3x + 2y = 16 and 7x + y = 19.

Back

(2, 5)