Systems of Equations - Elimination/Substitution

Front

What is a system of equations?

Back

A set of two or more equations with the same variables that are solved together.

Front

What does it mean to solve a system of equations?

Back

Finding the values of the variables that satisfy all equations in the system simultaneously.

Front

What is the elimination method?

Back

A technique for solving systems of equations by adding or subtracting equations to eliminate one variable.

Front

What is the substitution method?

Back

A technique for solving systems of equations by solving one equation for one variable and substituting that expression into the other equation.

Front

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

Back

If the equations represent parallel lines, they will never intersect, indicating no solution.

Front

How do you determine if a system of equations has infinitely many solutions?

Back

If the equations represent the same line, every point on the line is a solution, indicating infinitely many solutions.

Front

Solve the system: 4x + 9y = 28 and -4x - y = -28.

Back

(7, 0)

Front

Solve by elimination: 4x + 4y = 4 and 3x + 4y = 10.

Back

(-6, 7)

Front

Solve: y = -1x - 5 and 4x - 8y = 4.

Back

(-3, -2)

Front

What is the solution to this system: x = 7 - 2y and 2x + y = 5?

Back

(1, 3)