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〔2x-3y=-8 〔9x+2y=-5 (5,6) (0,-4) (1,-7) (-2,1) Solution

User BigDaddy
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1 Answer

7 votes

Answer:

Solution: x = -1; y = 2

Explanation:

Method to solve: Elimination:

Solving for x:

  • We can begin by multiplying first equation by 2 and the second equation by 3.

This will allow us to eliminate y when adding the equations since -6y + 6y = 0:

Multiplying 2x - 3y = 8 by 2:

2(2x - 3y = -8)

4x - 6y = -16

Multiplying 9x + 2y = -5 by 3:

3(9x + 2y = -5)

27x + 6y = -15

Now we can add the two equations to eliminate y and solve for x:

4x - 6y = -16

+

27x + 6y = -15

----------------------------------------------------------------------------------------------------------(4x + 27x) + (-6y + 6y) = (-16 - 15)

(31x = -31) / 31

x = -1

Thus, x = -1.

Solving for y:

Now we can solve for y by plugging in -1 for x in the first equation (2x - 3y = -8):

2(-1) - 3y = -8

(-2 - 3y = -8) + 2

(-3y = -6) / -3

y = 2

Thus, y = 2.

Checking the validity of the answers:

Now we can check that our answers are correct by plugging in -1 for x and 2 for y in both equations and seeing if we get the same answer on both sides of the equation:

Checking -1 for x and 2 for y in 2x - 3y = -8:

2(-1) - 3(2) = -8

-2 - 6 = -8

-8 = -8

Checking -1 for x and 2 for y in 9x + 2y = -5:

9(-1) + 2(2) = -5

-9 + 4 = -5

-5 = -5

Thus, our answer are correct.

User Iryna Prokopenko
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