Please answer the following questions pertaining to the functions. Show your work! Given the equation 2x-3y=12 A) Determine if the solution(s) if the equation is paired with 3x+2y=31
B) Determine if the solution(s) if the equation is paired with 6x-9y=11
C) What types of slopes do parallel lines have?

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  A) (x, y) = (9, 2)

  B) no solution

  C) the same slope

Step-by-step explanation:

A) In the attached, the given equation is graphed in red. The paired equation is shown in blue. They intersect at the point (9, 2), which is the solution to this system of paired equations.

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B) The line is parallel to its paired line, so there is NO SOLUTION.

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C) Parallel lines have the same slope.

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Additional comments

A graphing calculator provides a quick and easy solution to a system of equations. There are many calculators and apps and on-line sites that can solve a system of equations for you.

For the pair of equations in part A, you can eliminate the y-variable by adding 2 times the first equation to 3 times the second equation:

  2(2x -3y) +3(3x +2y) = 2(12) +3(31)   ⇒   13x = 117   ⇒   x = 9

Substituting in the first equation gives ...

  2(9) -3y = 12   ⇒   6 -y = 4   ⇒   y = 2

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For the paired equation in part B, the ratio of the x- and y-coefficients is 6/-9 = -2/3, the same as it is for the given equation. The constants are different (even after dividing the second equation by 3), so the lines are parallel (not coincident). This means the system of paired equations has no solution.

step-by-step explanation: