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Linear Sentences in Two Variables

February 14, 2012 454 No of hits
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Linear Sentences in Two Variables

Solving linear sentences with two variables can be intimidating to students. Variables are frightening enough, but solving for two variables is a downright dreaded topic in high school math.

To begin, let's first review linear equations. A linear equation is an equation that forms a straight line when plotted on a graph. You will not find any squares, cubes, cube roots, square roots, etc., in linear equations. A linear equation only contains constants and variables raised to the first power. Since the first power is understood, remember you won't actually see an exponent of 1. All linear equations can be written in the form ax + b = 0.

Here is an example of an equation you will be asked to solve with two variables:

Solve for x, if y = 2.

2x - 4y = 22

Plug the value 2 into the equation for the variable x:

2x - 4y = 22

2x - (4)(2) = 22

2x - 8 = 22

Using the order of operations, multiple 4 by 2 first. Next, add 8 to both sides of the equation before solving for x.

2x - 8 = 22

2x = 30

X = 15

You will also be given a system of equations. Here is an example:

2x - y = 12

X - y = 2

X + y = 18

To start, solve the first equation for y. You could choose x as well, but it is easier to choose y since the variable has no coefficient in front.

2x - y = 12

- y = -2x + 12

y= 2x - 12

Next, plug the value of y (2x -12) into the next two equations.

x - y = 2

x - (2x -12) = 2

x - 2x + 12 = 2

-x + 12 = 2

-x = -10

x = 10

And the next equation:

x + y = 18

x + 2x -12 = 18

3x -12 = 18

3x = 30

x = 10

Now you can find the value of y by plugging the value for x (10) into any of the three equations.

2x - y = 12

2 (10) - y = 12

20 - y = 12

-y = -8

y = 8

Or:

x - y = 2

10 -y = 2

-y = -8

y = 8

Or:

x + y = 18

10 + y = 18

y = 8

To check your answers, plug both values into the equations.

2x - y = 12

(2)(10) - 8 = 12

Does 20 - 8 = 12? YES!

And:

x - y = 2

10 - 8 = 2

Does 10 - 8 = 2? YES!

And:

x + y = 18

10 + 8 = 18

Does 10 + 8 = 18? YES.

By checking your answers in all three equations, you can guarantee you have the correct solutions for the variables.

Tags:   Linear sentences in two variables   Algebra 2   Linear sentences   Linear equations  

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Solving linear sentences with two variables can be intimidating to students. Variables are frightening enough, but solving for two variables is a downright dreaded topic in high school math.

To begin, let's first review linear equations. A linear equation is an equation that forms a...

By: Richard Martine Created 74 months ago

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    February 23, 2013
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