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Solve the system by using the addition (elimination) method.

Solve the system by using the addition (elimination) method.-example-1
User Linval
by
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1 Answer

2 votes

Answer:

x = -4; y = 12

Explanation:

Step 1: Multiply the first equation by 4 and the second equation by -7:

4(7x - 2y = -52)

-7(4x + 7y = 68)

---------------------------------------------------------------------------------------------------------- 28x - 8y = -208

-28x - 49y = -476

Step 2: Add the two equations to cancel the xs:

(28x + (-28x)) + (-8y + (-49y)) = (-208 + (-476))

-57y = -684

Step 3: Divide both sides by -57 to find y:

y = 12

Step 4: Plug in 12 for y in the first equation to find x:

7x - 2(12) = -52

7x - 24 = -52

Step 5: Add 24 to both sides:

(7x - 24 = -52) + 24

7x = -28

Step 6: Divide both sides by 7 to find x:

(7x = -28) / 7

x = -4

Thus, y = 12 and x = -4

Optional Step 7: Check the validity of our answers:

We can check that our answers are correct by plugging in 12 for y and -4 for x in both equations in our system and see whether we get -52 for the first equation and 68 for the second equation:

Checking answers for the first equation:

7(-4) - 2(12) = -52

-28 - 24 = -52

-52 = -52

Checking answers for the second equation:

4(-4) + 7(12) = 68

-16 + 84 = 68

68 = 68

Thus, our answers are correct.

User Vidha
by
8.7k points

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