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Drag each label to the correct location on the image.Identify which equations have one solution, infinitely many solutions, or no solution. 3u + 40 + 2u = 6u - 30 - u2.2z + 3z = 4.5 - 3.24/5x + 2/3 + 1/5x = x2.3y + 3.2 - y = 2.1 + 1.3y + 1.12/3x + 2/3 + 1/5x = 2/3x20 + 4r = 32 - 2r

User Martianwars
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1 Answer

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You have to identify if the following equations have one solution, infinitely many solutions, or no solution.

3u + 40 + 2u = 6u - 30 - u simplify similar terms both sides

5u + 40 = 5u - 30 subtract 5u both sides

40 = - 30

The previous result is an indetermination, hence, the equation does not have solution

2.2z + 3z = 4.5 - 3.2 simplify similar terms

5.2z = 1.3 divide 5.2 both sides

z = 1.3/5.2

z = 0.25

Hence, this equation has one solution

4/5x + 2/3 + 1/5x = x simplify similar terms

5/5 x + 2/3 = x

x + 2/3 = x subtract x both sides

2/3 = 0

The previous result is an indetermination, hence, the equation does not have solution

2.3y + 3.2 - y = 2.1 + 1.3y + 1.1 simplify similar terms both sides

1.3y + 3.2 = 1.3y + 3.2 subtract 1.3y both sides

3.2 = 3.2

The previous result means that the equation has infinite solutions.

2/3x + 2/3 + 1/5x = 2/3x simplify similar terms both sides

19/15 x + 2/3 = 2/3 x subtract 2/3x both sides

3/5 x + 2/3 = 0 subtract 2/3 both sides

3/5 x = - 2/3 multiply by 5/3 both sides

x = -10/9

Hence, the previoues equation has one solution

20 + 4r = 32 - 2r​ add 2r both sides

20 + 4r + 2r = 32

20 + 6r = 32 subtract 20 both sides

6r = 32 - 20 simplify

6r = 12 divide by 6 both sides

r = 12/6

r = 2

Hence, the previous equation has one solution

User Abhiram Mishra
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