Systems of Equations: Substitution Method

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 point(s) where the equations intersect.

Tags

CCSS.8.EE.C.8B

CCSS.HSA.REI.C.6

Front

What is the substitution method?

Back

The substitution method is a technique for solving systems of equations by solving one equation for one variable and substituting that expression into the other equation.

Tags

CCSS.8.EE.C.8B

CCSS.HSA.REI.C.6

Front

How do you solve for y in the equation y = 3x - 8?

Back

To solve for y, simply substitute a value for x into the equation. For example, if x = 2, then y = 3(2) - 8 = -2.

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CCSS.HSF.IF.A.2

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.

Tags

CCSS.8.EE.C.8B

CCSS.HSA.REI.C.6

Front

Given the equations y = 3x - 8 and y = 4 - x, how do you find the solution?

Back

Set the two expressions for y equal to each other: 3x - 8 = 4 - x. Solve for x, then substitute back to find y.

Tags

CCSS.8.EE.C.8B

CCSS.HSA.REI.C.6

Front

What does it mean if two equations have no solution?

Back

If two equations have no solution, it means they are parallel lines that never intersect.

Tags

CCSS.8.EE.C.8A

Front

What does it mean if two equations have infinitely many solutions?

Back

If two equations have infinitely many solutions, it means they represent the same line, and every point on the line is a solution.

Tags

CCSS.8.EE.C.8A

Front

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

Back

Substitute the solution back into both original equations to see if both equations are satisfied.

Tags

CCSS.8.EE.C.8B

CCSS.HSA.REI.C.6

Front

Solve the system using substitution: y = 2x + 3 and y = -x + 1. What is the solution?

Back

The solution is (2, 7).

Tags

CCSS.8.EE.C.8B

CCSS.HSA.REI.C.6

Front

What is the significance of the point of intersection in a system of equations?

Back

The point of intersection represents the values of the variables that satisfy all equations in the system.

Tags

CCSS.8.EE.C.8B