# Algebra

y =1/4x - 4 : y = -7/4x + 4

I need help with this one...has to be solved by elimination. Thanks

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1. multiply 1st eqn by 7

add to 2nd eqn to eliminate x

solve for y , then substitute back to find x

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2. y = y

1 / 4 x - 4 = - 7 / 4 x + 4

Add 7 / 4 x to both sides

1 / 4 x - 4 + 7 / 4 x = - 7 / 4 x + 4 + 7 / 4 x

8 / 4 x - 4 = 4

2 x - 4 = 4

2 x - 4 + 4 = 4 + 4

2 x = 8

Divide both sides by 2

x = 8 / 2

x = 4

Replace this value in equation for y.

y = 1 / 4 x - 4 = x / 4 - 4 = 4 / 4 - 4 = 1 - 4 = - 3

OR

y = - 7 / 4 x + 4 = - 7 ∙ x / 4 + 4 = - 7 ∙ 4 / 4 + 4 = - 7 + 4 = - 3

Solution:

x = 4 , y = - 3

You can write this as:

( 4 , - 3 )

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3. -x/4 + y = -4. Standard form.
Multiply both sides by 4:
Eq1: -x + 4y = -16.

7x/4 + y = 4.
Multiply both sides by 4:
Eq2: 7x + 4y = 16.

Multiply Eq1 by -1 and add Eq1 and Eq2:
x - 4y = 16
7x + 4y = 16
Sum: 8x = 32
X = 4.
In Eq1, replace X with 4 and solve for Y:
-4 + 4y = -16.
Y = -3.

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