The solution to the given system of equations is x = 62/7 and y = 10. These values satisfy both equations, providing a consistent solution to the system.
To solve the given system of equations:
2x = 8 + 2y
0 = 4 - 3x - y
Follow these steps:
Step 1: Rearrange the Equations
2x - 2y = 8
3x + y = 4
Step 2: Multiply the Equations by 2
4x - 4y = 16
3x + y = 4
Step 3: Add the Equations
Adding the two equations to eliminate y:
7x - 3y = 20
Step 4: Solve for x
Now, solve for x:
7x = 3y + 20
x = (3/7)y + (20/7)
Step 5: Substitute into the First Equation
Substitute the expression for x into the first equation:
2((3/7)y + (20/7)) - 2y = 8
(6/7)y + (40/7) - 2y = 8
(6/7)y - (14/7) = 8
(6/7)y = (14/7) + 8
(6/7)y = (70/7)
y = 10
Step 6: Substitute y into the Expression for x
Now that we know y, substitute it back into the expression for x:
x = (3/7)(10) + (20/7)
x = 62/7
Final Answer:
The solution to the system of equations is x = 62/7 and y = 10.