Solving Systems by Substitution

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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. The solution to the system is the set of values that satisfy all equations simultaneously.

Tags

CCSS.8.EE.C.8B

CCSS.HSA.REI.C.6

Front

What does it mean to solve a system of equations by substitution?

Back

Solving a system of equations by substitution involves solving one of the equations for one variable and then substituting that expression into the other equation.

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CCSS.8.EE.C.8B

CCSS.HSA.REI.C.6

Front

How do you isolate a variable in an equation?

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To isolate a variable, you perform algebraic operations to get the variable on one side of the equation and all other terms on the opposite side.

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CCSS.7.EE.B.4A

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What is the first step in solving the system of equations x + 2y = 8 and 3x - y = 5 by substitution?

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The first step is to solve one of the equations for one variable. For example, you can solve the first equation for x: x = 8 - 2y.

Tags

CCSS.8.EE.C.8B

CCSS.HSA.REI.C.6

Front

What is the solution to the system of equations x + 2y = 8 and 3x - y = 5?

Back

The solution is (2, 3), meaning x = 2 and y = 3.

Tags

CCSS.HSA.REI.C.9

Front

What is the graphical representation of a system of equations?

Back

The graphical representation of a system of equations is the point(s) where the graphs of the equations intersect. Each intersection point represents a solution to the system.

Tags

CCSS.8.EE.C.8B

Front

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

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If two lines are parallel, it means that the system of equations has no solution, as the lines never intersect.

Tags

CCSS.8.EE.C.8A

Front

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

Back

If two lines coincide, it means that the system of equations has infinitely many solutions, as every point on the line is a solution.

Tags

CCSS.8.EE.C.8A

Front

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

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

Tags

CCSS.8.EE.C.8B

CCSS.HSA.REI.C.6

Front

What is the substitution method used for?

Back

The substitution method is used to solve systems of equations, particularly when one equation can be easily solved for one variable.

Tags

CCSS.8.EE.C.8B

CCSS.HSA.REI.C.6