Chapter 5.1-2 Systems of Equations Review

Front

What is a system of equations?

Back

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

Front

What does it mean for a system of equations to have no solution?

Back

It means the lines represented by the equations are parallel and never intersect.

Front

What is the graphical representation of a solution to a system of equations?

Back

The point where the lines intersect on a graph.

Front

How can you solve a system of equations by graphing?

Back

By plotting both equations on the same graph and identifying the intersection point.

Front

What is substitution in the context of 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 does it mean for a system of equations to have infinitely many solutions?

Back

It means the equations represent the same line, so 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

What is the slope-intercept form of a linear equation?

Back

y = mx + b, where m is the slope and b is the y-intercept.

Front

What is the solution to the system: y = -1/4x + 4 and y = 2x + 2?

Back

(A) The solution is the point where the two lines intersect.

Front

How do you solve the system: 5x + 4y = -14 and y = -7x - 15 by substitution?

Back

Substituting y from the second equation into the first gives the solution (-2, -1).