Explain how you would create opposite terms for the x-
variable in this system.
3x - 6y = -8

-1/3x+ 4y = 6

Your answer would be, You can use the Elimination Method, by Multiplying, One or Both Equations by a Constant.

Solve System of Linear Equation:

3x - 6y = -8, -1/4x + 4y = 6 > y = 32 /21; x = 8 / 21

Steps:

[ 3x - 6y = -8, -1 / 4x + 4y = 6 ]

Isolate x for 3x - 6y = -8: x = -8 + 6y / 3

3x - 6y = -8

Add 6y both sides:

3x - 6y + 6y = -8 + 6y

Simplify:

3x = - 8 + 6y

Divide Both sides by 3:

3x / x = -8 / 3 + 6y / 3

Simplify:

x = -8 + 6y / 3

Substitute:

x = -8 + 6y / 3

[ 1 / 4 * -8 + 6y / 3 + 4y = 6 ]

Isolate:

-1 / 4 -8 + 6y / 3 + 4y = 6

y = 32 / 21

For x = -8 + 6y / 3

Substitute:

y = 32 / 21

x = -8 + 6 / 3 * 32 / 21

-8 + 6 / 3 * 32 / 21

x = 8 / 21

The Solution to the Systems of Equations are: y = 32 / 21; x = 8 / 21

Hope that helps!!! : )

Sample Response: To create opposite terms for the x-variable, you need to multiply the second equation by a number that will result in the x term becoming –3x. That number would need to be a multiple of the denominator, which is 3. Multiplying the second equation by 9 would create opposite terms for the x-variable.

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