Question

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

Answer 1

Are you sure

Answer 2

To solve this system of equations using the elimination method, we will multiply the first equation by 2 to create coefficients that will allow us to eliminate y.

First equation:
2x + y = 3.5

Second equation:
- x + 2y = 2.5

Multiplying the first equation by 2:
4x + 2y = 7

Now, we can add the second equation to the first equation to eliminate y:

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

This simplifies to:
3x + 4y = 9.5

Now we have a new equation:

3x + 4y = 9.5

Next, we will solve this equation for y:

4y = 9.5 - 3x
y = (9.5 - 3x)/4

Substituting this value of y back into the first equation:

2x + (9.5 - 3x)/4 = 3.5

Multiplying every term by 4 to eliminate the fraction:

8x + 9.5 - 3x = 14

Combining like terms:

5x + 9.5 = 14

Subtracting 9.5 from both sides:

5x = 14 - 9.5
5x = 4.5

Dividing both sides by 5:

x = 4.5/5
x = 0.9

Now that we have found the value of x, we can substitute it back into one of the original equations to solve for y:

2(0.9) + y = 3.5
1.8 + y = 3.5
y = 3.5 - 1.8
y = 1.7

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

Answer 3

Yes, I am sure. By following the steps of the elimination method, we obtain x = 0.9 and y = 1.7 as the solution to the system of equations.