# Solve the system of equations : 6x + 5y = 5, 3x - 10y = 15

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### 4 Answers

The system of equations to be solved is

6x + 5y = 5 ...(1)

3x - 10y = 15 ...(2)

From (1)

x = (5 - 5y)/6

substitute this for x in (2)

=> 3*(5 - 5y)/6 - 10y = 15

=> (5 - 5y) - 20y = 30

=> -25y = 25

=> y = -1

As x = (5 - 5y)/6 = (5 + 5)/6 = 10/6

**The solution of the given equations is x = 5/3 and y = -1**

You should use either elimination method or substitution method to solve the system.

I suggest to use elimination method to remove the variable y.

You need to multiply the first equation by 2 such that:

`12x + 10y = 10`

You need to add this new equation to the second equation of system such that:

`12x + 10y + 3x - 10y = 10 + 15`

Adding like variables yields:

`15x = 25`

Dividing by 5 both sides yields: `3x = 5 =gt x = 5/3`

`` You need to plug `x = 5/3` in any of the two original equation of the system.

Picking the second equation yields:

`3*(5/3) - 10y = 15 =gt 5 - 10y = 15`

`-10y = 15-5 =gt -10y = 10 =gt y = -1`

**Hence, the solution to the system of simultaneous equations is `x=5/3; y = -1` .**

The elimination method.

(1) 6x + 5y = 5

(2) 3x - 10y = 15

(3) Multiply equation (1) by 2

12x + 10y = 10

(4) Add equation (2) and (3)

15x = 25

Now its single variable and you can solve for x.

Plug this value into one of the above equations and solve for y.

First, we sum them up,

6x + 5y = 5 --> 12x + 10y = 10

12x + 10y = 10

3x - 10y = 15

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

12x + 3x + 10y - 10y = 25

15x = 25

x= 25/15 = 5/3

Then, we substitude x in to one of the equations(it doesn't matter which one you substitude).

3 ( 5/3) - 10y = 15

5 - 10y = 15

-10y = 10

y = -1

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

x = 5/3, y= -1