What is the solution set of the given system of equations 2y = x + 3 and 5y = x - 7?

Solution:

Given: Equations are 2y = x + 3

5y = x - 7

The given equation can be rewritten as

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

5y - x = - 7 --- (2)

Using the elimination method, let us eliminate the variable x.

Now multiply equation (2) by -1, we get

-5y + x = 7

2y - x = 3

By adding these equations

-3y = 10

y = -10/3

Substitute the value of y = -10/3 in equation (1)

2y - x = 3

2(-10/3) - x = 3

-20/3 - x = 3

By further calculation,

x = - 20/3 - 3

Taking LCM

x = (-20 - 9)/3

x = -29/3

Therefore, the solution to the set of equations is (-29/3, -10/3).

What is the solution set of the given system of equations 2y = x + 3 and 5y = x - 7?

Summary:

The solution set of the given system of equations 2y = x + 3 and 5y = x - 7 is (-29/3, -10/3).