Solving Systems Using Substitution

Front

What is a system of equations?

Back

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

Front

What does it mean if a system of equations has one solution?

Back

It means the graphs of the equations intersect at exactly one point.

Front

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

Back

It means the graphs of the equations are parallel and never intersect.

Front

What does it mean if a system of equations has infinite solutions?

Back

It means the equations represent the same line, so every point on the line is a solution.

Front

What is the substitution method in solving systems of equations?

Back

The substitution method involves solving one equation for one variable and substituting that expression into the other equation.

Front

How do you determine the number of solutions from the equations y=8x+1 and y=6x+3?

Back

By graphing or solving, you find that they intersect at (1, 9), indicating one solution.

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What does the equation 0 = 0 represent in a system of equations?

Back

It represents infinite solutions, as it is always true.

Front

What is the graphical representation of a system of equations?

Back

The graphical representation shows the lines of the equations on a coordinate grid.

Front

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

Back

Isolate one variable in one of the equations.

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What is the difference between a system of equations and a single equation?

Back

A system of equations involves multiple equations that share variables, while a single equation has only one.