SOLUTION: Solve the following equations and word problems using any method (for problems with two unknowns, make sure to use two answers): 1.4x + 7y = 7 6x

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Question 33719: Solve the following equations and word problems using any method (for problems with two unknowns, make sure to use two answers):
1.4x + 7y = 7
6x - 7y = 6
2. 1/5 x + 1/3y = -4
x-y = -6
3. 3x = 4 - 4y
2x - 4y = 5
4. The length of a rectangular swimming pool is 11 feet longer than the width. If the perimeter is 75 feet, then what is the length and width of the rectangle?

Answer by sarah_adam(201) (Show Source):
You can put this solution on YOUR website!
1)
4x + 7y = 7 --- eq 1
6x - 7y = 6 --- eq 2
------------
10x = 13 --- eq 1 + eq 2
x = 13/10 = 1.3
substitute value of x in eq 1
4(1.3)+7y = 7
5.2 + 7y = 7
7y = 7 - 5.2 = 1.8
y = 1.8/7 = 0.2571

2)
1/5 x + 1/3y = -4 --- eq 1
x-y = -6 --- eq 2
5x + 3y = 1/4 = 0.25 --- eq 1
x - y = -6 --- eq 2

5x + 3y = 0.25 --- eq 1
3x - 3y = -18 --- eq 2 (multipling the entire equation with 2)
----------------
8x = - 17.75
x = -17.75/8 = -2.219
substitute the value of x in eq 2
y = x+6
y = -2.129+6 = 3.871

In the same way you can solve the third set of equations

4}The length of a rectangular swimming pool is 11 feet longer than the width. If the perimeter is 75 feet, then what is the length and width of the rectangle?
Let the length of the rectangular field be L and width be W
Given :
L = W+11
P = 75ft
but we know P = 2(L+W)
75 = 2(W+11+W)
37.5 = 2W + 11
2W = 26.5
W = 26.5/2 = 13.25ft
So L = 13.25 +11 = 24.25 ft
L = 24.25 ft
W = 13.25 ft

SOLUTION: Solve the following equations and word problems using any method (for problems with two unknowns, make sure to use two answers): 1.4x + 7y = 7 6x - 7y = 6 2. 1/5 x + 1/3y =