Solving Systems of Equations by Graphing or Substitution

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 graphical method of solving systems of equations?

Back

Plotting the equations on a graph and identifying the point(s) where they intersect.

Front

What is substitution in solving systems of equations?

Back

Replacing one variable with an expression from another equation to solve for the variables.

Front

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

Back

The system has no solution because the lines never intersect.

Front

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

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

Front

How do you determine the solution of a system of equations graphically?

Back

The solution is the point where the two lines intersect on the graph.

Front

What is the first step in solving a system of equations by substitution?

Back

Solve one of the equations for one variable in terms of the other.

Front

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

Back

(2, 0) is the solution.

Front

How do you write the substituted equation for y = 4x in 5y - 2x = 18?

Back

5(4x) - 2x = 18.