Solve the following system of equations using the elimination method.
2x + y = 3.5, -x + 2y = 2.5
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To solve the system of equations using the elimination method, we need to eliminate one variable by multiplying one or both of the equations by a constant. In this case, let's eliminate the variable x.
To eliminate the variable x, we need to multiply the first equation by -1 and the second equation by 2. This will make the coefficient of x in both equations equal to -2.
(-1)(2x + y) = (-1)(3.5)
2x + y = -3.5
2(-x + 2y) = 2(2.5)
-2x + 4y = 5
Now, we can add the two new equations together to eliminate x:
(2x + y) + (-2x + 4y) = (-3.5) + 5
2x - 2x + y + 4y = -3.5 + 5
5y = 1.5
Now we can solve for y by dividing both sides of the equation by 5:
5y/5 = 1.5/5
y = 0.3
Now that we have the value of y, we can substitute it back into one of the original equations to solve for x. Let's use the first equation:
2x + y = 3.5
2x + 0.3 = 3.5
2x = 3.5 - 0.3
2x = 3.2
x = 3.2/2
x = 1.6
So the solution to the system of equations is (x, y) = (1.6, 0.3)