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Triss [41]
3 years ago
5

Which value, when placed in the box, would result in a system of equations with infinitly many solutions? Y=2x - 5 2y-4x=

Mathematics
1 answer:
Nezavi [6.7K]3 years ago
6 0

Given:

The system of equations is

y=2x-5

2y-4x=?

To find:

The missing value for which the given system of equations have infinitely many solutions.

Solution:

Let the missing value be k.

We have,

y=2x-5

2y-4x=k

Taking all the terms on the left side, the given equations can be rewritten as

-2x+y+5=0

-4x+2y-k=0

The system of equations a_1x+b_1y+c_1=0 and a_2x+b_2y+c_2=0 have infinitely many solutions if

\dfrac{a_1}{a_2}=\dfrac{b_1}{b_2}=\dfrac{c_1}{c_2}

We have,

a_1=-2,b_1=1,c_1=5

a_2=-4,b_2=2,c_2=-k

Now,

\dfrac{-2}{-4}=\dfrac{1}{2}=\dfrac{5}{-k}

\dfrac{1}{2}=\dfrac{1}{2}=\dfrac{5}{-k}

\dfrac{1}{2}=\dfrac{5}{-k}

On cross multiplication, we get

-k=10

k=-10

Therefore, the missing value is -10.

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