Math, asked by hasini3127, 2 months ago

What is the value of y? 5x–2y=4 and 10x–4y=8.

Answers

Answered by djarodiya1981
3

Step-by-step explanation:

Solve by Substitution 5x+2y=4 , 10x+4y=8

5

x

+

2

y

=

4

,

10

x

+

4

y

=

8

Solve for

x

in the first equation.

Subtract

2

y

from both sides of the equation.

5

x

=

4

2

y

10

x

+

4

y

=

8

Divide each term by

5

and simplify.

Divide each term in

5

x

=

4

2

y

by

5

.

5

x

5

=

4

5

+

2

y

5

10

x

+

4

y

=

8

Cancel the common factor of

5

.

Cancel the common factor.

5

x

5

=

4

5

+

2

y

5

10

x

+

4

y

=

8

Divide

x

by

1

.

x

=

4

5

+

2

y

5

10

x

+

4

y

=

8

Move the negative in front of the fraction.

x

=

4

5

2

y

5

10

x

+

4

y

=

8

Replace all occurrences of

x

in

10

x

+

4

y

=

8

with

4

5

2

y

5

.

x

=

4

5

2

y

5

10

(

4

5

2

y

5

)

+

4

y

=

8

Simplify

10

(

4

5

2

y

5

)

+

4

y

Simplify each term.

Apply the distributive property.

x

=

4

5

2

y

5

10

(

4

5

)

+

10

(

2

y

5

)

+

4

y

=

8

Cancel the common factor of

5

Factor

5

out of

10

.

x

=

4

5

2

y

5

5

(

2

)

(

4

5

)

+

10

(

2

y

5

)

+

4

y

=

8

Cancel the common factor.

x

=

4

5

2

y

5

5

(

2

(

4

5

)

)

+

10

(

2

y

5

)

+

4

y

=

8

Rewrite the expression.

x

=

4

5

2

y

5

2

4

+

10

(

2

y

5

)

+

4

y

=

8

Multiply

2

by

4

.

x

=

4

5

2

y

5

8

+

10

(

2

y

5

)

+

4

y

=

8

Cancel the common factor of

5

Move the leading negative in

2

y

5

into the numerator.

x

=

4

5

2

y

5

8

+

10

(

2

y

5

)

+

4

y

=

8

Factor

5

out of

10

.

x

=

4

5

2

y

5

8

+

5

(

2

)

(

2

y

5

)

+

4

y

=

8

Cancel the common factor.

x

=

4

5

2

y

5

8

+

5

(

2

(

2

y

5

)

)

+

4

y

=

8

Rewrite the expression.

x

=

4

5

2

y

5

8

+

2

(

2

y

)

+

4

y

=

8

Multiply

2

by

2

.

x

=

4

5

2

y

5

8

4

y

+

4

y

=

8

Combine the opposite terms in

8

4

y

+

4

y

...

Add

4

y

and

4

y

.

x

=

4

5

2

y

5

8

+

0

=

8

Add

8

and

0

.

x

=

4

5

2

y

5

8

=

8

Since

8

=

8

, the equation will always be true.

x

=

4

5

2

y

5

Always true

Remove any equations from the system that are always true.

x

=

4

5

2

y

5

Thank you

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