Solving Systems of Linear Equations - short period

Front

What is a system of linear equations?

Back

A set of two or more linear equations with the same variables.

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.

Front

What is the elimination method?

Back

A technique for solving systems of equations by adding or subtracting equations to eliminate a 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

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

Back

The lines represented by the equations are parallel and never intersect.

Front

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

Back

The equations represent the same line, meaning every point on the line is a solution.

Front

How do you determine if a system has one solution?

Back

If the lines intersect at exactly one point, the system has one solution.

Front

Solve by elimination: -x + y = -13 and -8x - 4y = -8

Back

(5, -8)

Front

Solve by substitution: 4x - 3y = 5 and y = 2x - 3

Back

(2, 1)

Front

Solve by elimination: 4x - 6y = -6 and -2x - 12y = -12

Back

(0, 1)