Systems of Equations: Substitution/Graphing

Front

What is a system of equations?

Back

A set of two or more 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 substitution method?

Back

A method for solving a system of equations by solving one equation for one variable and substituting that expression into the other equation.

Front

What is the graphing method?

Back

A method for solving a system of equations by graphing the equations on the same coordinate plane and identifying the point(s) of intersection.

Front

What does it mean if two lines are parallel in a system of equations?

Back

The system has no solutions because the lines never intersect.

Front

What does it mean if two lines coincide in a system of equations?

Back

The system has infinitely many solutions because the lines are the same.

Front

How do you isolate a variable in an equation?

Back

Rearranging the equation to get the variable on one side and the constants on the other.

Front

What is the solution to the system of equations x - 2y = 1 and x + 4y = 7 when y = 1?

Back

x = 3.

Front

What is the solution to the system of equations 8x + 4y = 12 and y = -2x + 3?

Back

The variable y is isolated.

Front

What is the solution to the system of equations represented by the graph of two intersecting lines?

Back

The coordinates of the intersection point represent the solution.