Question

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

Answer 1

Answer:

$( \frac{5}{11} \:, - \frac{3}{11} )$

Step-by-step 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

$\frac{22x}{22} = \frac{10}{22}$

Calculate

$x = \frac{5}{11}$

Now, substitute the given value of x into the equation

y = -3 + 6x

$y = - 3 + 6 \times \frac{5}{11}$

Solve the equation for y

$y = - \frac{3}{11}$

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

$(x ,\: y) = ( \frac{5}{11} ,\: - \frac{3}{11} )$

-----------------------------------------------------------

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

$6 \times \frac{5}{11} - ( - \frac{3}{11} ) = 3$

$4 \times \frac{5}{11 } + 3 \times ( - \frac{3}{11} ) = 1$

Simplify the equalities

$3 = 3$

$1 = 1$

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

$( \: x ,\: y \: ) = ( \frac{5}{11} \:, - \frac{3}{11} )$

Hope this helps..

Best regards!!

Answer 2

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