Question

Find the solution for this system of equations.

12x + 15y = 34
-6x + 5y = 3

x =
y =
Please help. What is the x and the y?

Answer 1

Step-by-step explanation:

Given :

• 12x + 15y = 34

• -6x + 5y = 3

To Find :

• Find the solution for this system of equations.

Solution :

• 12x + 15y = 34 ........ Equ ( 1 )

• -6x + 5y = 3 ........ Equ ( 2 )

According to the Equ ( 2 ) :

➭ - 6x + 5y = 3

2 Multiplying both side :

➭ 2 ( -6x + 5y ) = 2 × 3

• -12x + 10y = 6.........Equ ( 3 )

Substract the Equ ( 3 ) to ( 1 )

12x + 15y = 34

-12x + 10y = 6

____________

25y = 40

_____________

➭ y = 40 / 25

➭ y = 8/5

Substitute the all value in Equ ( 1 )

➭ 12x + 15 × 8 /5 = 34

➭ 12x + 120/5 = 34

➭ 12x + 24 = 34

➭ 12x = 34 - 24

➭ 12x = 10

➭ x = 10 / 12

➭ x = 5 /6

• Hence the Value of x = 5 / 6 And y = 8/5

Answer 2

Answer: The value of x is $\frac{5}{6}$ and value of y is $\frac{8}{5}$.

Step-by-step explanation:

Given:We have given linear equations $12x + 15y = 34$ and $-6x + 5y = 3$ respectively.

To find:We have to find the value of x and y.

Explanation:

Step 1:The given linear equations are,

                                  $12x + 15y = 34$   ............. $(1)$  

                                  $-6x + 5y = 3$    .............. $(2)$

Step 2:From equation (2) find out the value of y,

⇒                                 $-6x + 5y = 3$

⇒                                            $5y = 3+ 6x$

⇒                                              $y = \frac{3 + 6x}{5}$............$(3)$

Step 3:From equation (3) substitute the value of y in equation (1),we have,

⇒                                 $12x + 15y = 34$

⇒                         $12x + 15(\frac{3 + 6x)}{5} = 34$

⇒                        $12x + 3(3 + 6x) = 34$

⇒                           $12x + 9 + 18x = 34$

⇒                                     $30x + 9 = 34$

⇒                                           $30x = 34-9$

⇒                                           $30x = 25$

⇒                                               $x = \frac{25}{30}$

⇒                                               $x = \frac{5}{6}$.................$(4)$

∴ The value of x is $\frac{5}{6}$.

Step 4:From equation (4) substitute the value of x in equation (2).We have,

⇒                                   $-6x + 5y = 3$

⇒                                $-6(\frac{5}{6} ) + 5y = 3$

⇒                                     $- 5 + 5y = 3$

⇒                                              $5y = 3 + 5$

⇒                                              $5y = 8$

⇒                                                $y = \frac{8}{5}$

∴ The value of y is $\frac{8}{5}$.

Concept:The substitution method is the algebraic method to solve simultaneous linear equations. As the word says, in this method, the value of one variable from one equation is substituted in the other equation. In this way, a pair of the linear equation gets transformed into one linear equation with only one variable, which can then easily be solved.

Steps of Substitution Method:

1)Simplify the given equation by expanding the parenthesis.

2)Solve one of the equations for either x or y.

3)Substitute the step 2 solution in the other equation.

4)Now solve the new equation obtained using elementary arithmetic operations.

Finally, solve the equation to find the value of the second variable

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