Solving Linear Systems by Elimination

Front

What is a linear system?

Back

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

Front

What does it mean if a linear system has no solution?

Back

It means that the equations represent parallel lines that never intersect.

Front

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

Back

It means that the equations represent the same line, so every point on the line is a solution.

Front

What is the elimination method for solving linear systems?

Back

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

Front

How do you determine the number of solutions in a linear system?

Back

By analyzing the slopes and intercepts of the lines represented by the equations.

Front

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

Back

Align the equations so that corresponding variables and constants are in the same columns.

Front

Solve for x and y: x + y = 0, -x - y = 0

Back

Infinitely Many Solutions

Front

Solve for x and y: x + y = 5, -(x - 3y = 3)

Back

(4.5, 0.5)

Front

Solve for x and y: x + y = 90, 2x - y = 105

Back

(65, 25)

Front

How many steps are there for solving a system of equations by elimination?

Back

5