Final answer:
To find x+y for the given system of equations, we use the elimination method, solve for x and y individually, and then add the calculated values to find that x+y equals 1.
Step-by-step explanation:
To find the value of x+y, we need to solve the system of equations:
4x+5y=6
4x-3y=-10
We can solve this system by elimination or substitution. Let's use elimination:
Multiply the second equation by 5 to make the coefficients of y in both equations the same:
20x-15y=-50
Now, subtract the second equation from the first equation:
(4x+5y) - (20x-15y) = 6 - (-50)
Simplify:
-16x + 20y = 56
From here, we can solve for y by isolating it:
20y = 16x + 56
Divide both sides by 20:
y = (16/20)x + 56/20
Simplify:
y = (4/5)x + 14/5
Now, substitute this expression for y back into one of the original equations. Let's use the first equation:
4x + 5((4/5)x + 14/5) = 6
Simplify:
4x + 4x + 14 = 6
Combine like terms:
8x + 14 = 6
Subtract 14 from both sides:
8x = -8
Divide both sides by 8:
x = -1
Now, substitute this value of x back into the expression for y:
y = (4/5)(-1) + 14/5
Simplify:
y = -4/5 + 14/5
Combine like terms:
y = 10/5
Simplify:
y = 2
Therefore, x+y = -1 + 2 = 1.