Solve using the elimination method. Show your work. If the system has no solution or an infinite number of solutions, state this.2x + 2y = 202x – 2y = 4
note that in elimination method, we first simplify/modify one (or both) the given equation until if we add the two given equation, one of the variables will cancel out. in the problem, we can obviously see that the 2y in the first equation will be cancelled out by the -2y of the second. adding them:
2x + 2y = 20
2x – 2y = 4
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4x = 24
x = 6
now we substitute this value of x to either equation to get y. let's substitute this to first equation:
2x + 2y = 20
2(6) + 2y = 20
12 + 2y = 20
2y = 8
y = 4
hope this helps~ :)
To solve the given system of equations using the elimination method, we need to eliminate one variable by adding or subtracting the two equations.
Given system of equations:
2x + 2y = 20
2x - 2y = 4
To eliminate the variable "y", we will add the two equations together.
(2x + 2y) + (2x - 2y) = 20 + 4
Simplifying, we get:
2x + 2y + 2x - 2y = 24
Combining like terms, we get:
4x = 24
Dividing both sides by 4, we find:
x = 6
Now, substitute the value of x back into either equation to solve for y. Let's use the first equation:
2(6) + 2y = 20
Simplifying:
12 + 2y = 20
Subtracting 12 from both sides:
2y = 8
Dividing both sides by 2:
y = 4
Therefore, the solution to the system of equations is x = 6 and y = 4.
To check our answer, substitute these values into the original equations:
For the first equation: 2(6) + 2(4) = 20 --> 12 + 8 = 20 (True)
For the second equation: 2(6) - 2(4) = 4 --> 12 - 8 = 4 (True)
Both equations are satisfied, so our solution is correct.
Therefore, the solution to the system of equations is x = 6 and y = 4.