Question

Solve the system of equations.

2.5y + 3x = 27
5x – 2.5y = 5
What equation is the result of adding the two equations?
What is the solution to the system?

Answer 1

If you put them together, +2.5y and -2.5y neutralize themselves while 5x and 3x become 8x.

2.5y + 3x = 27

5x – 2.5y = 5

8x = 32

x = 4

2.5y + 3x4 = 27

2.5y + 12 = 27

2.5y = 27-12

2.5y = 15

y = 15/2.5

y = 6

X = 4

Y = 6

Answer 2

The result of adding the two equations is:

`8x=32`

And the solution to the system is (4, 6).

Explanation:

We are given the system of equations:

`\left\{ \begin{array} \ 2.5y+3x=27 \\ 5x-2.5y=5 \end{array}`

We can solve by elimination. If we add the two equations together, we acquire:

`(2.5y+3x)+(5x-2.5y)=(27+5)`

Simplifying yields:

`(2.5y-2.5y)+(3x+5x)=(32)`

Combine like terms. Therefore, we the two equations are added together, we obtain:

`8x=32`

Solve for x by dividing both sides by 8:

`x=4`

With the value of x, we can solve for y. Using the first equation:

`2.5y+3x=27`

Substitute 4 for x and solve for y:

`\displaystyle \begin{aligned} 2.5y + 3(4) & = 27 \\ \\ 2.5y + 12 & = 27 \\ \\ 2.5y & = 15 \\ \\ y & = 6 \end{aligned}`

In conclusion, our solution to the system is (4, 6).