Question

Solve the following system of equations using the elimination method. 2x+y=3.5 , −x+2y=2.5 (1 point) (,)

Answer 1

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)