Math, asked by sammy6638, 1 year ago

5x-2y=4;x+8y=26 find the value x+y

Answers

Answered by Inflameroftheancient
21

Hey there!

Solving the given equation by substitution:

Given equation:  5x - 2y = 4,  x + 8y = 26.

5x - 2y = 4 --- [1]

x + 8y = 26 --- [2]

Solving and isolating the variable of "x" for the equation 5x - 2y = 4.

Add "2y" to both the given sides.

5x - 2y + 2y = 4 + 2y

Simplify the equation.

5x = 4 + 2y

Divide the equations in both sides by a value of "5" :

\bf{\frac{5x}{5} = \frac{4}{5} + \frac{2y}{5}} \\

Simplify the equation.

\bf{x = \frac{4 + 2y}{5}} \\

Now, substitute the value of "x" into the "second equation".

\bf{\frac{4 + 2y}{5} + 8y = 26} \\

Multiplying bot the sides by the value of "5".

\bf{\frac{4x + 2y}{5} \times 5 + 8y \times 5 = 26 \times 5} \\

Refine the equation to it's totality'

4 + 2y + 40y = 130

4 + 42y = 130

Subtracting from value "4" on both the sides.

4 + 42y -4 = 130 -4

Simplify the equation.

42y = 126

Divide the following sides by a value of "42" to cancel out the value in L.H.S and obtain value in R.H.S.

\bf{\frac{42y}{42} = \frac{126}{42}} \\

Therefore, simplify the value and get the value of "y".

\boxed{\bf{\therefore \: \: y = 3}} \\

Now, for finding the value of variable "x", substitute the value of "y = 3".

\bf{x = \frac{4 + 2 \times 3}{5}} \\

Multiply the numbers: 2 * 3 = 6 and, Add the numbers 4 + 6 = 10.

\bf{\therefore \: \: x = \frac{10}{5}} \\

Divide the numbers of "10" and "2" = 5.

\boxed{\bf{\therefore \: \: x = 2}} \\

The following variable values are for this system of equations in this context:

\boxed{\huge{\bf{y = 3 \: and \: x = 2}}} \\

Hope this helps you and clears the doubts for solving two provided equations!

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