Question

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

A. No solution
B. Infinitely many solutions
C. (-16,6)
D. (-16,-2)

Answer 1

Answer: 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 :

`2x+y=1~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~(i)\\\\3x-y=-6~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~(ii)`

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

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

`(2x+y)+(3x-y)=1+(-6)\\\\\Rightarrow 5x=-5\\\\\Rightarrow x=-(5)/(5)\\\\\Rightarrow x=-1.`

From equation (i), we get

`2*(-1)+y=1\\\\\Rightarrow -2+y=1\\\\\Rightarrow y=1+2\\\\\Rightarrow y=3.`

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

Answer 2

Equations:
2x+y=1 ..............(1)
3x-y=-6...............(2)

The two equations have different slopes -2, 3, so there is a unique solution.

Add (1) & (2)
2x+3x = -5 => x=-1
Substitute x=-1
into (1) : 2(-1)+y=1 => y=3
into (2) : 3(-1)-y = -6 => y=3 checks.
=>
The solution is (-1,3).

Note: None of the above answer choices fit, so please check for typos.