# What is the solution to this system of linear equations? 2x + y = 1 3x – y = –6 (–1, 3)

###### Question:

## Answers

x,y x→ 1.04, y →5.72 i hope this helps

(-1,3) is the answer to that

2x + y = 1 . . . (1)

3x - y = -6 . . . (2)

(1) + (2) => 5x = -5 => x = -5/5 = -1

From (1), 2x - 1 = 1 => 2x = 1 + 1 = 2 => x = 2/2 = 1

x = 1, y = -1

5x= -5 so x=-1 and y= 1-2(-1)= 3

(–1, 3)

Step-by-step explanation:

The given system of linear simultaneous equations is expressed as

2x + y = 1 - - - - - - - - - - -1

3x – y = –6 - - - - - - - - - -2

We would eliminate y by adding equation 1 to equation 2. It becomes

2x + 3x = 1 - 6

5x = - 5

Dividing the left hand side and the right hand side of the equation by 5, it becomes

5x/5 = - 5/5

x = - 1

Substituting x = - 1 into equation 1, it becomes

2 × - 1 + y = 1

- 2 + y = 1

Adding 2 to the left hand side and the right hand side of the equation, it becomes

- 2 + 2 + y = 1 + 2

y = 3

Answer is (-1, 3)

Step-by-step explanation:

2x + y = 1 ...equation 1

3x - y= -6 ... equation 2

Add equation 1 and 2 together

(2x + y) + (3x -y) = 1 - 6

2x + 3x + y - y = -5

5x = -5

Dividing both sides by 5,

x = -1

Substitute for X = -1 in any of the equations, (As an example, I am using equation 1, (2x + y = 1)

2(-1) + y = 1

-2 + y = 1

Add 2 to both sides

-2 + 2 + y = 1 + 2

y = 3.

x = -1, y = 3.

CHECK.

Using equation 2, (3x - y = -6)

Substitute for the value of X = -1 and y = 3

3(-1) - (3) =

-3 - 3 = -6.

(-1, 3)

Step-by-step explanation:

Only the first question is complete.

You want to solve ...

2x +y = 1

3x -y = -6

You can add these two equations to get ...

5x = -5

x = -1 . . . . . divide by 5

This matches the first choice: (-1, 3).

The correct option is (A) (-1, 3).

Step-by-step explanation: We are given to solve the following system of linear equations. :

[tex]2x+y=1~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~(1)\\3x-y=-6~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~(2)[/tex]

We will be using the method of ELIMINATION ot solve the given system.

Adding equations (1) and (2), we get

[tex](2x+y)+(3x-y)=1+(-6)\\\\\Rightarrow 5x=1-6\\\\\Rightarrow 5x=-5\\\\\Rightarrow x=-\dfrac{5}{5}\\\\\Rightarrow x=-1.[/tex]

Putting the value of x in equation (1), we get

[tex]2\times(-1)+y=1\\\\\Rightarrow -2+y=1\\\\\Rightarrow y=1+2\\\\\Rightarrow y=3.[/tex]

Thus, the required solution of the given system is x = -1 and y = -3.

Option (A) is CORRECT.

The required solution is (x, y) = (-1, 3).

Step-by-step explanation: We are given to find the solution to the following system of equations :

[tex]2x+y=1~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~(i)\\\\3x-y=-6~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~(ii)[/tex]

We will be using the method of Elimination to solve the given system.

Adding equations (i) and (ii), we get

[tex](2x+y)+(3x-y)=1+(-6)\\\\\Rightarrow 5x=-5\\\\\Rightarrow x=-\dfrac{5}{5}\\\\\Rightarrow x=-1.[/tex]

From equation (i), we get

[tex]2\times(-1)+y=1\\\\\Rightarrow -2+y=1\\\\\Rightarrow y=1+2\\\\\Rightarrow y=3.[/tex]

Thus, the required solution is (-1, 3).

(-1,3)

Step-by-step explanation:

2x + y = 1 (i)

3x - y = -6 ... (ii)

Solving the simultaneous equations (i) and (ii) using elimination method;

We add (i) and (ii) to get;

5x = -5 , x = -1

And y = 1 - 2(-1) = 1 + 2 = 3

So the solution is (-1,3).