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What is x+y?
4x+5y=6
4x-3y=-10

User Erdogant
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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.

User Tiramonium
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