Systems of Equations

Substitution Method

Solve the following system of equations using the substitution method:

2 x + 3 y = 12

and

x = y + 4

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Addition/Elimination Method

Solve the following system of equations using the Addition/Elimination method:

3 x - 2 y = 4

and

2 x + 3 y = - 1

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Determining Perpendicular Lines

Find the equation of the line perpendicular to the line

2 x - 3 y = 6

and passing through the point

(1, 2)

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Graphing Method

Solve the system of equations using the graphing method:

y = 2 x + 3

and

y = - x + 1

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Determining if the Point is a Solution

Determine if the point (2,5) is a solution to the system of equations:

2 x + 3 y = 16

and

x + 4 y = 18

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Finding the Constant of Variation

Consider the system of equations

3 x - y = 12

and

k x - 2 y = 24

, where

k

is the constant of variation. If the system has no solution, what is the value of

k

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Dependent, Independent, and Inconsistent Systems

Solve the following system of equations:

2 x + 3 y = 6

and

4 x + 6 y = 12

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Finding the Union (or)

Find the union of the solutions to the following system of equations: \n 1.

2 x + y = 10

\n 2.

x - y = 3

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Finding the Equation with Real Coefficients

Find the equations of the lines that pass through the point (1,2) and are tangent to the circle with equation

x^{2} + y^{2} = 25

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Finding a Direct Variation Equation

Find the direct variation equation of a system of equations where

y = 3 x + 2

and

y = 5 x - 1

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Finding the Slope for Every Equation

Solve the following system of equations, and find the slope for each equation:

\begin{matrix} 2 x + 3 y = 6 5 x - 4 y = - 2 \end{matrix}

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Finding a Variable Using the Constant of Variation

Given the direct variation equation

y = k x

, where

y = 8

when

x = 4

, and a system of equations where

2 x + 3 y = 10

and

5 x - y = 15

, find the value of

k

and the solutions to the system of equations.

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Substitution Method

Addition/Elimination Method

Determining Perpendicular Lines

Graphing Method

Determining if the Point is a Solution

Finding the Constant of Variation

Dependent, Independent, and Inconsistent Systems

Finding the Union (or)

Finding the Equation with Real Coefficients

Finding a Direct Variation Equation

Finding the Slope for Every Equation

Finding a Variable Using the Constant of Variation

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