Question

Determine whether the system of linear equations has one and only one solution, infinitely many solutions, or no solution.

Answer 1

Answer:

only one solution

Step-by-step explanation:

Complete question:

Determine whether the system of linear equations has one and only one solution, infinitely many solutions, or no solution. 2x − y = 2 3x + y = −6 one and only one solution infinitely many solutions no solution Find the solution, if one exists. (If there are infinitely many solutions, express x and y in terms of the parameter t. If there is no solution, enter NO SOLUTION.) (x, y) =

Given the expression

2x − y = 2 .... 1

3x + y = −6  ..... 2

We are to determine the number of solution the equation has:

Add equation 1 and 2

2x + 3x = 2 - 6

5x = -4

x = -4/5

Substitute x = -4/5 into 1

From 1: 2x − y = 2 .... 1

2(-4/5) - y = 2

-8/5 - y = -2

-y = -2+8/5

-y = -10+8/5

-y = -2/5

y = 2/5

Since the value of x and y are just 1 hence the system of equations has ine solution