Solve using elimination method. If the system has no system or infinite number of solutions, state this. Please show all work. I need to show how I came about my answer. I need this as soon as possible please. I would appreciate any and all help!!
2x+2y=20
2x-2y=4
add the equations, and get...
4x=20 or x=5, then figure y
2x+2y=20
2x-2y=4
_________
4y= 16
y=16
2x+2(40)=20
2x+8=20
2x=12
x=6
(x,y)= (6,4)
Is this correct???
how would one know whether the answer is correct?
Plug your values for x and y into both equations and see whether the equations hold.
In this case, your answer is correct.
To solve this system of equations using the elimination method, we can eliminate one variable by adding or subtracting the equations.
Given:
Equation 1: 2x + 2y = 20
Equation 2: 2x - 2y = 4
Step 1: Multiply one or both equations by a constant to make the coefficients of one of the variables equal.
Let's multiply Equation 2 by -1 to eliminate x:
-1(2x - 2y) = -1(4)
This simplifies to:
-2x + 2y = -4
Now we have:
Equation 1: 2x + 2y = 20
Equation 2: -2x + 2y = -4
Step 2: Add the two equations together to eliminate the x variable:
(2x + 2y) + (-2x + 2y) = 20 + (-4)
This simplifies to:
4y = 16
Step 3: Solve for y by dividing both sides of the equation by the coefficient of y:
4y/4 = 16/4
y = 4
Step 4: Substitute the value of y back into one of the original equations to solve for x.
Using Equation 1: 2x + 2(4) = 20
2x + 8 = 20
2x = 20 - 8
2x = 12
x = 12/2
x = 6
Therefore, the solution to the system of equations is x = 6, y = 4.
Since we were able to find a unique solution for both x and y, the system of equations has a single solution.