Systems of Linear Equations and Inequalities

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 for a system of equations to have one solution?

Back

The lines representing the equations intersect at exactly one point.

Front

What is the substitution method in solving systems of equations?

Back

A method where one equation is solved for one variable, and that expression is substituted into the other equation.

Front

What is the elimination method in solving systems of equations?

Back

A method where equations are added or subtracted to eliminate one variable, making it easier to solve for the other.

Front

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

Back

The lines representing 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 the number of solutions in a system of equations?

Back

By analyzing the slopes and y-intercepts of the lines represented by the equations.

Front

Solve the system: 2x + 3y = 12 and 5x - y = 13.

Back

(3, 2)

Front

Solve the system by substitution: 5x + 4y = -14 and y = -7x - 15.

Back

(-2, -1)

Front

In a pasture, there are horses and chickens. If there are a total of 28 animals and 80 legs, how many chickens and horses are there?

Back

12 horses, 16 chickens.