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 elimination mean in the context of systems of equations?

Back

Elimination is a method for solving systems of equations by removing one variable, allowing the other variable to be solved directly.

Front

How do you eliminate a variable in a system of equations?

Back

To eliminate a variable, you can add or subtract the equations after multiplying them by suitable coefficients to make the coefficients of one variable equal.

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

What does it mean if a system of equations has no solution?

Back

A system has no solution if the equations represent parallel lines that never intersect.

Front

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

Back

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

Front

Solve by elimination: 12x + 36y = -3 and -12x - 36y = 0.

Back

No solution.

Front

Solve by elimination: 4x + 8y = 20 and -4x + 2y = -30.

Back

(7, -1).

Front

Solve by elimination: -6x + 5y = 1 and 6x + 4y = -10.

Back

(-1, -1).

Front

Solve by elimination: -8x - 10y = 20 and -8x - 6y = -4.

Back

(5, -6).