Question

Solve the following system of equations using the elimination method.

2x+y=3.5
,  −x+2y=2.5


(1 point)

Answer 1

[AI-generated answer — Bot GPT 3.5]

To solve the system of equations using the elimination method, we will eliminate one variable by adding or subtracting the equations.

To eliminate the variable x, let's multiply the first equation by 2 and the second equation by -1:

2(2x + y) = 2(3.5)
-1(-x + 2y) = -1(2.5)

This gives us:

4x + 2y = 7
x - 2y = -2.5

Now we can add the equations together to eliminate y:

4x + 2y + x - 2y = 7 + (-2.5)

Simplifying this equation:

5x = 4.5

Dividing both sides by 5:

x = 0.9

Now substitute this value of x back into one of the original equations (let's use the first one):

2(0.9) + y = 3.5
1.8 + y = 3.5

Subtracting 1.8 from both sides:

y = 1.7

Therefore, the solution to the system of equations is x = 0.9 and y = 1.7.