Question

The substitution method solve 6x-y=3 4x+3y=1

Answer 1

y= - 3 + 6x
4x+3y=1
4x+3(-3 + 6x) = 1
4x-9+18x-1=0
22x= 0
22x= -8
x = -8/22 = -4/11

Answer 2

`( (5)/(11) \:</strong><strong>,</strong><strong> - (3)/(11) )`

Explanation:

6x - y = 3

4x + 3y = 1

Solve the equation for y

y = -3 + 6x

4x + 3y = 1

Substitute the given value of y into the equation

4x + 3y = 1

plug the value

`4x + 3( - 3 + 6x) = 1`

Distribute 3 through the parentheses

`4x - 9 + 18x = 1`

Collect like terms

`22x - 9 = 1`

Move constant to R.H.S and change its sign

`22x = 1 + 9`

Calculate the sum

`22x = 10`

Divide both sides of the equation by 22

`(22x)/(22) = (10)/(22)`

Calculate

`x = (5)/(11)`

Now, substitute the given value of x into the equation

y = -3 + 6x

`y = - 3 + 6 * (5)/(11)`

Solve the equation for y

`y = - (3)/(11)`

The possible solution of the system is the ordered pair ( x , y )

`(x </strong><strong>,</strong><strong>\: y) = ( (5)/(11) </strong><strong>,</strong><strong>\: - (3)/(11) )`

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Check if the given ordered pair is the solution of the system of equations

`6 * (5)/(11) - ( - (3)/(11) ) = 3`

`4 * (5)/(11 ) + 3 * ( - (3)/(11) ) = 1`

Simplify the equalities

`3 = 3`

`1 = 1`

Since all of the equalities are true , the ordered pair is the solution of the system

`( \: x </strong><strong>,</strong><strong>\: y \: ) = ( (5)/(11) \:</strong><strong>,</strong><strong> - (3)/(11) )`

Hope this helps..

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