Math 1: CW 5.3 Systems of Equations (Elimination)

Front

What is a system of equations?

Back

A system of equations is a set of two or more equations with the same variables. The solution is the point(s) where the equations intersect.

Front

What does it mean to solve a system of equations by elimination?

Back

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

Front

What is the elimination method?

Back

The elimination method is a technique used to solve systems of equations by removing one variable, allowing for easier calculation of the remaining variable.

Front

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

Back

A system has no solution if the equations represent parallel lines, which means they never intersect.

Front

What does it mean if a system of equations has infinite solutions?

Back

A system has infinite solutions if the equations represent the same line, meaning every point on the line is a solution.

Front

Solve the system by elimination: x + y = 10, x - y = 2

Back

(6, 4)

Front

Solve the system by elimination: 2x + 3y = 6, 4x + 6y = 12

Back

Infinite solutions

Front

Solve the system by elimination: 3x + 4y = 10, 3x - 2y = 4

Back

(2, 1)

Front

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

Back

The first step is to align the equations and decide which variable to eliminate.

Front

How can you make the coefficients of one variable the same in both equations?

Back

You can multiply one or both equations by a number to make the coefficients of one variable equal.