Systems of Equations--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. The solution is the set of values that satisfy all equations simultaneously.

Front

What is the substitution method in solving systems of equations?

Back

The substitution method involves solving one equation for one variable and then substituting that expression into the other equation(s) to find the values of the variables.

Front

How do you isolate a variable in an equation?

Back

To isolate a variable, you perform inverse operations to get the variable on one side of the equation by itself.

Front

What does it mean to solve for x and y in a system of equations?

Back

Solving for x and y means finding the values of x and y that make both equations true at the same time.

Front

What is the first step in using the substitution method?

Back

The first step is to solve one of the equations for one variable in terms of the other variable.

Front

If you have the equations y = 2x + 3 and 4x - y = 1, how would you use substitution?

Back

You would substitute 2x + 3 for y in the second equation: 4x - (2x + 3) = 1.

Front

What is the solution to the system of equations y = 2x + 3 and 4x - y = 1?

Back

The solution is (1, 5), meaning x = 1 and y = 5.

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

Back

A system has no solution if the equations represent parallel lines that never intersect.

Front

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

Back

A system has infinite solutions if the equations represent the same line, meaning every point on the line is a solution.

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How can you check your solution for a system of equations?

Back

You can check your solution by substituting the values of x and y back into the original equations to see if they hold true.