## 17Calculus Precalculus - Use Elimination to Solve Systems of Linear Equations

##### 17Calculus

Solve by Elimination

This is the best technique to solve systems of equations since it works all the time, you can control the numbers to avoid fractions until near the end of the solution and it will prepare you for the fourth technique using matrices. So it is important to learn this technique well.
Here is a good video explaining this technique while working an example, AND he explains why this technique works.

### Khan Academy - Solving Systems of Equations by Elimination [12min-43secs]

video by Khan Academy

Okay, this technique is pretty straight-forward, so we are going to let you jump right into the practice problems.

Practice

Unless otherwise instructed, solve these linear systems using elimination.

$$2x+3y=4$$
$$-2x+7y=16$$

Problem Statement

$$2x+3y=4$$
$$-2x+7y=16$$

Solution

### PatrickJMT - 1719 video solution

video by PatrickJMT

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$$x-3y=6$$
$$4x-3y=10$$

Problem Statement

$$x-3y=6$$
$$4x-3y=10$$

Solution

### PatrickJMT - 1720 video solution

video by PatrickJMT

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$$4x-2y=16$$
$$5x+2y=11$$

Problem Statement

$$4x-2y=16$$
$$5x+2y=11$$

Solution

### MIP4U - 1721 video solution

video by MIP4U

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$$4x+3y=8$$
$$x-3y=7$$

Problem Statement

$$4x+3y=8$$
$$x-3y=7$$

Solution

### MIP4U - 1724 video solution

video by MIP4U

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$$3x+5y=4$$
$$-2x+3y=10$$

Problem Statement

$$3x+5y=4$$
$$-2x+3y=10$$

Solution

### MIP4U - 1725 video solution

video by MIP4U

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$$2x-3y=-1$$
$$-4x+6y=5$$

Problem Statement

$$2x-3y=-1$$
$$-4x+6y=5$$

Solution

### MIP4U - 1726 video solution

video by MIP4U

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$$5x+2y=4$$
$$5x+2y=-2$$

Problem Statement

$$5x+2y=4$$
$$5x+2y=-2$$

Solution

### MIP4U - 1727 video solution

video by MIP4U

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$$3x+y=-10; 7x+5y=-18$$

Problem Statement

$$3x+y=-10; 7x+5y=-18$$

Solution

### MIP4U - 1728 video solution

video by MIP4U

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$$2x=-6y+8$$
$$3x-5y=2$$

Problem Statement

$$2x=-6y+8$$
$$3x-5y=2$$

$$(13/7,5/7)$$

Problem Statement

$$2x=-6y+8$$
$$3x-5y=2$$

Solution

The instructor in this video runs out of time and does not finish the problem. He gets $$y=5/7$$ and then stops. Using his work, here is how to get the final answer.
Substituting $$y=5/7$$ into the first original equation, we have
$$\begin{array}{rcl} 2x & = & -6y+8 \\ 2x & = & -6(5/7)+8 \\ 2x & = & -30/7+56/7 \\ 2x & = & 26/7 \\ x & = & 13/7 \end{array}$$

$$(13/7,5/7)$$

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$$4x-4y+8z=20; 8x+4y-4z=4; 12x-8y-12z=-40$$

Problem Statement

$$4x-4y+8z=20; 8x+4y-4z=4; 12x-8y-12z=-40$$

Solution

### PatrickJMT - 1722 video solution

video by PatrickJMT

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$$2x-y+z=3; 5x+2y-3z=1; 2x+y-z=2$$

Problem Statement

$$2x-y+z=3; 5x+2y-3z=1; 2x+y-z=2$$

Solution

### PatrickJMT - 1723 video solution

video by PatrickJMT

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