Systems of Equations: Substitution/Graphing

Front

What is a system of equations?

Back

A set of two or more equations with the same variables that are solved together.

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What does it mean to solve a system of equations?

Back

Finding the values of the variables that satisfy all equations in the system simultaneously.

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 graphing method in solving systems of equations?

Back

A method where each equation is graphed on the same coordinate plane, and the point of intersection represents the solution.

Front

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

Back

It means there is no solution to the system, as the lines never intersect.

Front

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

Back

It means there are infinitely many solutions, as the lines overlap completely.

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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?

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

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How can you find the y-coordinate of the solution in a system of equations?

Back

By substituting the x-value of the solution into either equation to find the corresponding y-value.

Front

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

Back

Isolate one variable in one of the equations.