2x-2y=10
2x+y=5
y=-5
x=0 .
subtract the two equations
-3y = 5
y = -5/3
sub back into first equation
2x -2(-5/3) = 10
2x = 10 - 10/3
2x = 20/3
x = 10/3
To solve this system of equations, we can use the method of substitution or elimination. Let's use the method of substitution.
First, rearrange the equation 2x - 2y = 10 to isolate one variable in terms of the other variable. We can rewrite it as:
2x = 2y + 10
Next, solve the equation 2x + y = 5 for one variable. Rewrite it as:
y = 5 - 2x
Now, substitute the expression for y from the second equation into the first equation. Replace y with (5 - 2x):
2x = 2(5 - 2x) + 10
Simplify the equation:
2x = 10 - 4x + 10
Combine like terms:
2x + 4x = 20
6x = 20
Divide both sides by 6:
x = 20/6
Simplify the fraction:
x = 10/3
Now that we have the value of x, substitute it back into one of the original equations to find the value of y.
Using the equation 2x + y = 5:
2(10/3) + y = 5
Multiply:
20/3 + y = 5
Subtract 20/3 from both sides:
y = 5 - 20/3
To subtract 20/3 from 5, we need to get a common denominator. Multiply 5 by 3/3 to get 15/3:
y = 15/3 - 20/3
Subtract the fractions:
y = -5/3
Therefore, the solution to the system of equations is x = 10/3 and y = -5/3.