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Problem:

Solve each of the following systems of equations. Find all solutions.

(a)\(\begin{align*} x+y&=-1,\\ 3x &= 4-3y. \end{align*} \)

(b)\(\begin{align*} 3x - 4y + 2&=0,\\ 10 - 10y& = 10y - 15x. \end{align*}\)

 Feb 1, 2019
 #1
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the first one has no solutions, I will show you how, by step

1) we rewrite the equations : x+y=−1;3x=−3y+4

2) in the x+y=-1, we solve for x

x+y=−1

x+y+−y=−1+−y(Add -y to both sides)

x=−y−1

3)Substitute−y−1for x in 3x=−3y+4:

3x=−3y+4

3(−y−1)=−3y+4

−3y−3=−3y+4(Simplify both sides of the equation)

−3y−3+3y=−3y+4+3y(Add 3y to both sides)

−3=4

−3+3=4+3(Add 3 to both sides)

0=7

and so there are no solution

the second one:

1)Solve3x−4y+2=0 for x:

3x−4y+2=0

3x−4y+2+4y=0+4y(Add 4y to both sides)

3x+2=4y

3x+2+−2=4y+−2(Add -2 to both sides)

3x=4y−2

3x/3 = (4y-2)/3

(Divide both sides by 3)

x=4/3y + -2/3

Problem 2: Substitute 4/3y + -2/3 for x in -10y+10=15x-10

−10y+10=15x−10

−10y+10=15(4/3y+-2/3)-10

−10y+10=20y−20(Simplify both sides of the equation)

−10y+10+−20y=20y−20+−20y(Add -20y to both sides)

−30y+10=−20

−30y+10+−10=−20+−10(Add -10 to both sides)

−30y=−30

-30y/-30 = -30/-30, (Divide both sides by -30)

and Y=1

Now we solve for X

x=4/3y+-2/3

x=4/3(1) +-2/3

x=2/3

so x=2/3 and y=1

 Feb 1, 2019

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