Solving Linear Systems: Graphing, Substitution, Elimination

Front

What is a linear system?

Back

A linear system is a collection of two or more linear equations involving the same variables.

Front

What does it mean to solve a linear system?

Back

To solve a linear system means to find the values of the variables that satisfy all equations in the system simultaneously.

Front

What are the three main methods for solving linear systems?

Back

The three main methods are graphing, substitution, and elimination.

Front

How do you solve a linear system by graphing?

Back

To solve by graphing, plot each equation on the same coordinate plane and identify the point(s) where the lines intersect.

Front

What is substitution in solving linear systems?

Back

Substitution involves solving one equation for one variable and then substituting that expression into the other equation.

Front

What is elimination in solving linear systems?

Back

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

Front

What is the solution to the system of equations: x + y = 10 and x - y = 2?

Back

The solution is (6, 4).

Front

If a system of equations has no solution, what does that mean?

Back

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

Front

What does it mean if a system has infinitely many solutions?

Back

It means the equations represent the same line, and there are an infinite number of points that satisfy both equations.

Front

How can you check if your solution to a linear system is correct?

Back

You can substitute the solution back into the original equations to see if it satisfies all of them.