To find the values of x and y in the given system of equations:
1. Start by solving one of the equations for x or y. Let's solve the second equation for y:
4y = 2x - 8
Divide both sides of the equation by 4:
y = (2x - 8)/4
Simplify:
y = (1/2)x - 2
2. Substitute this value of y into the first equation:
3x - 8((1/2)x - 2) = 6
Distribute -8 to both terms inside the parentheses:
3x - 4x + 16 = 6
Combine like terms:
-x + 16 = 6
Subtract 16 from both sides of the equation:
-x = -10
Multiply both sides by -1 to solve for x:
x = 10
3. Substitute the value of x back into the second equation to find y:
4y = 2(10) - 8
Simplify:
4y = 20 - 8
4y = 12
Divide both sides by 4 to solve for y:
y = 3
So, the values of x and y are x = 10 and y = 3, respectively.
I hope this helps!