Question

Use the echelon method to solve the following system of two equations in two unknowns. Check your answer.

4x−3y=−1
−8x+6y=2
Select the correct choice below​ and, if​ necessary, fill in the answer box to complete your choice.
A.The solution is nothing.(Type an ordered​ pair.)
B.There are infinitely many solutions. The solution is nothing,y​,where y is any real number.
C. There is no solution.

Answer 1

To solve the system of equations using the echelon method, we can use the process of elimination to eliminate one variable at a time. The solution is infinitely many solutions, represented by y = any real number.

Step-by-step explanation:

To solve the system of equations using the echelon method, we can use the process of elimination to eliminate one variable at a time. Here are the steps:

1. Multiply the first equation by 2 to make the coefficients of x in both equations equal: 8x - 6y = -2
2. Add the second equation to the modified first equation: (8x - 6y) + (-8x + 6y) = -2 + 2
3. Simplify and solve for y: 0 = 0

Since 0 = 0, this means that the system of equations is consistent and dependent. Therefore, there are infinitely many solutions. The solution is y = any real number. In other words, the answer is B - There are infinitely many solutions.