Final answer:
To solve the system of equations 3x - 5y = 4 and -2x + 6y = 18, multiply Equation 1 by 2 and Equation 2 by 3 to eliminate the x term. Add the resulting equations and solve for y. Substitute the value of y back into the equations to solve for x. The solution is x = 14.25 and y = 7.75.
Step-by-step explanation:
The given equations are:
Equation 1: 3x - 5y = 4
Equation 2: -2x + 6y = 18
To solve this system of equations, we can use the method of substitution or elimination. Let's use the method of elimination:
Multiply Equation 1 by 2 and Equation 2 by 3 to eliminate the x term:
2(3x - 5y) = 2(4) --> 6x - 10y = 8
3(-2x + 6y) = 3(18) --> -6x + 18y = 54
Add the resulting equations:
(6x - 10y) + (-6x + 18y) = 8 + 54
-10y + 18y = 62
8y = 62
Solve for y:
y = 62/8 = 7.75
Substitute the value of y back into Equation 1 or Equation 2 to solve for x:
Using Equation 1:
3x - 5(7.75) = 4
3x - 38.75 = 4
3x = 42.75
x = 42.75/3 = 14.25
The solution to the system of equations is x = 14.25 and y = 7.75.