Question

Solve using the elimination method:
2x-3y=9 and x+4y=2

Answer 1

y = -5/11; x = 42/11

Explanation:

Step 1: Multiply the entire second equation by -2:

• We can solve by eliminating by first eliminating the xs.

Multiplying the second equation by -2 will allow us to eliminate the xs since 2x - 2x = 0:

-2(x + 4y = 2)

-2x - 8y = -4

Step 2: Add -2x - 8y = -4 and 2x - 3y = 9:

Now we can solve for y by adding the two equations and eliminating the xs:

2x - 3y = 9

+

-2x - 8y = -4

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(2x - 2x) + (-3y - 8y) = (9 - 4)

(-11y = 5) / -11

y = -5/11

Thus, y = -5/11.

Step 3: Solve for x by plugging in -5/11 for y in x + 4y = 2:

Now we can solve for x by plugging in -5/11 for y in x + 4y = 2:

x + 4(-5/11) = 2

(x - 20/11 = 2) + 20/11

x = 42/11

Thus, x = 42/11.

Optional Step 4: Check the validity of the answers:

Now we can check that our answers are correct by plugging in -5/11 for y and 42/11 for x in both equations and seeing if we the get the same answers on both sides:

Checking y = -5/11 and x = 42/11 in 2x - 3y = 9:

2(42/11) - 3(-5/11) = 9

84/11 + 15/11 = 9

99/11 = 9

9 = 9

Checking y = -5/11 and x = 42/11 in x + 4y = 2:

42/11 + 4(-5/11) = 2

42/11 - 20/11 = 2

22/11 = 2

2 = 2

Thus, our answers are correct.

Answer 2

x = 42/11

y = -5/11

Explanation:

multiply everything in the equation x+4y=2 by negative 2. now you have -2x -8y = -4. you can now cancel out the 2x in both equations. now you have -3y = 9 and -8y = -4. add now! -3y -8y = 9-4. -11y = 5, y = -5/11

now repeat the same process to find x.

multiply 2x-3y=9 by 4 - now you have 8x-12y=36. multiply x+4y=2 by 3, now you have 3x+12y=6. cancel out 12y and add the sides - so now 8x+3x=36+6. 11x = 42, therefore x = 42/11