josiemarie10
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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?

Respuesta :

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

xKelvin

Answer:

The result of adding the two equations is:

[tex]8x=32[/tex]

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

Step-by-step explanation:

We are given the system of equations:

[tex]\left\{ \begin{array} \ 2.5y+3x=27 \\ 5x-2.5y=5 \end{array}[/tex]

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

[tex](2.5y+3x)+(5x-2.5y)=(27+5)[/tex]

Simplifying yields:

[tex](2.5y-2.5y)+(3x+5x)=(32)[/tex]

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

[tex]8x=32[/tex]

Solve for x by dividing both sides by 8:

[tex]x=4[/tex]

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

[tex]2.5y+3x=27[/tex]

Substitute 4 for x and solve for y:

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

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

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