Systems of equations by 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 solving systems of equations?

Back

Elimination is a method used to solve systems of equations by removing one variable, allowing for 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

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

Back

(7, -1)

Front

Solve using elimination: 3x + 2y = -13 and 3x + 4y = 1.

Back

(-9, 7)

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

Solve using elimination: 5x + 16y = -16 and -9x - 8y = 8.

Back

(0, -1)

Front

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

Back

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

Front

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

Back

(5, -6)

Front

What is the solution to a system of equations?

Back

The solution is the set of values for the variables that make all equations in the system true.