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# Algebra

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What number must be placed in the box in the equation below to produce an equation that has more than one solution:

$1/2*y + 1/4 = 3 + \boxed{\phantom{400} } y$

Dec 22, 2021

### 1+0 Answers

#1
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first, re-write the equation in LaTeX.

$${1\over2}y+{1\over4}=3+\boxed{\phantom{400}}y$$

Instead of a box, substitute it for x.

$${1\over2}y+{1\over4}=3+xy$$

To get rid of the fractions, multiply both sides by 4.

$$4*({1\over2}y+{1\over4})=(3+xy)*4$$

simplified...

$$2y+1=12+4xy$$

move all numbers to one side

$$(2y+1)-(2y+1)=12+4xy-(2y+1)$$

simplified...

$$4xy-2y+11=0$$

the easiest way to get more than one solution is to make the equation a binomial.

to make $$4xy-2y+11=0$$ a binomial, we can just say that x=y

simplified...

$$4y^2-2y+11=0$$

since x=y, y must be placed in the box.

The only thing I am worried about is that it might not want a variable for the box, but instead an actual number.

Dec 23, 2021