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goldfiish [28.3K]
3 years ago
10

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

Mathematics
2 answers:
bekas [8.4K]3 years ago
8 0

Answer:

<h2> </h2><h2>( \frac{5}{11}  \:,  -  \frac{3}{11} )</h2>

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 )

<h2>(x ,\: y) = ( \frac{5}{11}  ,\:  -  \frac{3}{11} )</h2>

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

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

<h2>( \: x ,\: y \: ) = ( \frac{5}{11}  \:,  -  \frac{3}{11} )</h2>

Hope this helps..

Best regards!!

Juli2301 [7.4K]3 years ago
5 0
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
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