To solve the system of equations:
2x + 5y = 38 ----(1)
x - 3y = -3 ----(2)
We can use the method of substitution or elimination.
Let's solve the system using the method of substitution:
1. Solve equation (2) for x:
x = 3y - 3
2. Substitute the value of x from equation (2) into equation (1):
2(3y - 3) + 5y = 38
Simplify the equation:
6y - 6 + 5y = 38
11y - 6 = 38
Add 6 to both sides of the equation:
11y = 44
Divide both sides of the equation by 11:
y = 4
3. Substitute the value of y = 4 into equation (2) to find x:
x - 3(4) = -3
Simplify the equation:
x - 12 = -3
Add 12 to both sides of the equation:
x = 9
Therefore, the solution to the system of equations is x = 9 and y = 4.
This means that the point (9, 4) is the solution to the system of equations 2x + 5y = 38 and x - 3y = -3.