Solve the following system of linear equation using any algebraic method.

2x+5y=3
X-3y=7

x = 7 + 3y

2x + 5y = 3

Substitute 7+3y for x in second equation and solve for y. Insert that value into the first equation and solve for x. Check by inserting both values into the second equation.

To solve the system of linear equations:

1. Write down the given equations:
2x + 5y = 3 (Equation 1)
x - 3y = 7 (Equation 2)

There are several algebraic methods to solve a system of linear equations, such as substitution, elimination, or matrix algebra. Let's solve it using the method of elimination, also known as the addition method:

Step 1: Multiply each term of Equation 2 by 2 to make the coefficients of x in both equations the same:
2(x - 3y) = 2(7)
2x - 6y = 14 (Equation 3)

Step 2: Now, we will subtract Equation 3 from Equation 1 to eliminate the x terms:
(2x + 5y) - (2x - 6y) = 3 - 14
2x + 5y - 2x + 6y = -11
11y = -11

Step 3: Solve for y by dividing both sides of the equation by 11:
y = -11/11
y = -1

Step 4: Substitute y = -1 back into Equation 1 or Equation 2 to solve for x. Let's use Equation 2 for simplicity:
x - 3(-1) = 7
x + 3 = 7

Step 5: Solve for x:
x = 7 - 3
x = 4

Therefore, the solution to the given system of linear equations is x = 4 and y = -1.