Solve the following system of linear equation using any algebraic method.
2x+5y=3
X-3y=7
To solve the given system of linear equations, we can use the elimination or substitution method. Let's use the elimination method in this case.
Step 1: Multiply the second equation by 2 to make the coefficients of x in both equations the same.
2(x - 3y) = 2(7)
2x - 6y = 14
The modified system of equations becomes:
2x + 5y = 3 (Equation 1)
2x - 6y = 14 (Equation 2)
Step 2: Now, subtract Equation 2 from Equation 1.
(2x + 5y) - (2x - 6y) = 3 - 14
2x + 5y - 2x + 6y = -11
11y = -11
Dividing both sides of the equation by 11, we get:
y = -1
Step 3: Substitute the value of y (which is -1) back into one of the original equations to find the value of x. Let's use Equation 1:
2x + 5(-1) = 3
2x - 5 = 3
2x = 3 + 5
2x = 8
x = 8/2
x = 4
So, the solution to the system of equations is x = 4 and y = -1.
Therefore, the solution to the given system of linear equations is x = 4 and y = -1.