Solve the following system of equations using the elimination method. 2x+y=3.5 , −x+2y=2.5 (1 point) (,)
To solve the system of equations using the elimination method, we need to eliminate one of the variables by adding or subtracting the two equations.
The coefficients of x in the two equations are 2 and -1. To eliminate x, we can multiply the first equation by -1 and add it to the second equation.
-1(2x+y) + (-x+2y) = -1(3.5) + 2.5
-2x - y - x + 2y = -3.5 + 2.5
-3x + y = -1
Now we have a new equation -3x + y = -1.
To eliminate y, we can multiply the first equation by 2 and add it to the second equation.
2(2x+y) + (-x+2y) = 2(3.5) + 2.5
4x + 2y - x + 2y = 7 + 2.5
3x + 4y = 9.5
Now we have a new equation 3x + 4y = 9.5.
So the system of equations becomes:
-3x + y = -1
3x + 4y = 9.5
Now we can solve this system of equations. By adding the two equations together, the x variable will be eliminated.
(-3x + y) + (3x + 4y) = -1 + 9.5
y + 4y = 8.5
5y = 8.5
Dividing both sides by 5, we get:
y = 8.5/5
y = 1.7
Now we can substitute this value of y back into one of the original equations to solve for x.
2x + 1.7 = 3.5
2x = 3.5 - 1.7
2x = 1.8
Dividing both sides by 2, we get:
x = 1.8/2
x = 0.9
So the solution to the system of equations is: (0.9, 1.7)