Answer:
x=60 y=any real number
Explanation:
To find the values of x and y in the equation 2x + 4y = 120, we can use a method called substitution or elimination.
1. Substitution Method:
- Solve one of the equations for one variable in terms of the other variable. Let's solve the equation for x:
2x = 120 - 4y
x = (120 - 4y)/2
x = 60 - 2y
- Now, substitute the expression for x into the other equation:
2(60 - 2y) + 4y = 120
- Simplify and solve for y:
120 - 4y + 4y = 120
120 = 120
- Since the equation simplifies to 120 = 120, this means that y can take any value.
- Substitute the value of y back into the equation x = 60 - 2y to find x:
x = 60 - 2y
x = 60 - 2(0)
x = 60
- Therefore, the solutions for x and y are x = 60 and y can be any real number.
2. Elimination Method:
- Multiply the first equation by 2 to eliminate the x coefficient:
4x + 8y = 240
- Subtract the second equation from the modified first equation:
(4x + 8y) - (2x + 4y) = 240 - 120
2x + 4y = 120
- Now we have the same equation as the original. This means that y can take any value.
- Substitute the value of y into the original equation to find x:
2x + 4(0) = 120
2x = 120
x = 60
- So, the solutions for x and y are x = 60 and y can be any real number.
In summary, the values of x and y in the equation 2x + 4y = 120 are x = 60 and y can be any real number.