Question

Determine whether the s'ysten 2x-y=4 3x+y=-5 one and only one solutio

Answer 1

To determine whether the system of equations 2x - y = 4 and 3x + y = -5 has one and only one solution, we can solve the system using the method of substitution or elimination. By using the method of elimination, we find that the system has one solution: x = 7/9 and y = -25/3.

Step-by-step explanation:

To determine whether the system of equations 2x - y = 4 and 3x + y = -5 has one and only one solution, we can solve the system using the method of substitution or elimination. Let's use the method of elimination:

1. Multiply the equation 2x - y = 4 by 3 to eliminate the y variable: 6x - 3y = 12.
2. Add the equations 6x - 3y = 12 and 3x + y = -5 to eliminate the y variable: 9x = 7.
3. Divide both sides of the equation 9x = 7 by 9 to solve for x: x = 7/9.
4. Substitute the value of x into one of the original equations, let's use 3x + y = -5: 3(7/9) + y = -5.
5. Solve the equation for y: 21/9 + y = -5, y = -5 - 21/9, y = -54/9 - 21/9, y = -75/9, y = -25/3.

Therefore, the system of equations 2x - y = 4 and 3x + y = -5 has one solution, which is x = 7/9 and y = -25/3.