Substitution Method

Front

What is the substitution method in solving systems of equations?

Back

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

Front

How do you isolate a variable in an equation?

Back

To isolate a variable, you perform algebraic operations (addition, subtraction, multiplication, division) to get the variable on one side of the equation by itself.

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

Given the equations y = 3x + 14 and y = -4x, how do you solve for x?

Back

Set the two expressions for y equal to each other: 3x + 14 = -4x. Then solve for x.

Front

What does it mean to have a solution of (x, y) for a system of equations?

Back

A solution (x, y) means that both equations are satisfied when x and y are substituted into them.

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How can you check if your solution to a system of equations is correct?

Back

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

Front

What is the significance of the point (0, 2) in the context of the equation 4x + y = 2?

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The point (0, 2) is a solution to the equation, meaning that when x = 0, y equals 2, satisfying the equation.

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What is a system of equations?

Back

A system of equations is a set of two or more equations with the same variables that are solved simultaneously.

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

Back

If a system has no solution, it means that the equations represent parallel lines that never intersect.

Front

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

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If a system has infinitely many solutions, it means that the equations represent the same line, and every point on that line is a solution.