Solving Systems of Equations (All Methods)

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 to solve a system of equations?

Back

Finding the values of the variables that satisfy all equations in the system simultaneously.

Front

What is the substitution method?

Back

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

Front

What is the elimination method?

Back

A method for solving systems of equations by adding or subtracting equations to eliminate one variable.

Front

What does it mean for two lines to intersect?

Back

It means that the two equations have a common solution, represented by the coordinates of the intersection point.

Front

How can you check if a solution is correct for a system of equations?

Back

By substituting the solution back into both original equations to see if they hold true.

Front

What is the graphical method for solving systems of equations?

Back

Plotting the equations on a graph and identifying the point(s) where the lines intersect.

Front

What is the solution to the system of equations 3x + 2y = 16 and 7x + y = 19?

Back

(2, 5)

Front

What is the sum of the solutions to the system 3x + 2y = 16 and 7x + y = 19?

Back

7

Front

What is the solution to the system of equations y = 3x - 8 and y = 4 - x?

Back

(3, 1)