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Select the correct answer from the drop-down menu.
Find the solution set for the system of equations.

9x + 5y = 28

5x + 9y = 56

The solution set for the system of equations is 1. (-5/9, 0) 2. (-1/2, 13/2), 3. (0, 11/2), 4. (3, 9/2) .

Select the correct answer from the dropdown menu Find the solution set for the system of equations 9x 5y 28 5x 9y 56 The solution set for the system of equation class=

Respuesta :

joseaaronlara

Answer:

The answer to your question is 2. (-1/2, 13/2)

Step-by-step explanation:

Equation 1      9x + 5y = 28

Equation 2     5x + 9y = 56

Process

- Solve by Elimination

- Multiply equation 1 by 5 and equation 2 by -9

                   5(9x + 5y = 28)

                  -9(5x + 9y = 56)

           

                   45x + 25y = 140

                  -45x - 81y   = -504

                     0     -56y = -364

                                  y = -364/-56

                                 y = 13/2 = 6.5

- Find x

                     9x + 5(13/2) = 28

                     9x + 65/2 = 28

                     9x = 28 - 65/2

                     9x = -9/2

                       x = (-9/2)/9

                       x = -1/2

Answer:

2. [tex](-\frac{1}{2},\frac{13}{2})[/tex]

Step-by-step explanation:

Given Equations:

[tex]9x + 5y = 28[/tex]          Equation:1

[tex]5x + 9y = 56[/tex]           Equation:2

Multiplying Equation:1 by 5 and Equation:2 by 9, gives

[tex]45x+25y=140[/tex]    Equation:3

[tex]45x+81y=504[/tex]     Equation:4

Using Elimination Method, Subtract Equation:3 from Equation:4

[tex]45x+81y-(45x+25y)=504-140[/tex]

[tex]45x+81y-45x-25y=504-140[/tex]

[tex]56y=364[/tex]

[tex]y=\frac{364}{56}\\\\ y=6.5[/tex]  or [tex]y=\frac{13}{2}[/tex]

Putting, the value of 'y' in Equation:1

[tex]9x + 5y = 28\\9x + 5(6.5) = 28\\9x+32.5=28\\9x=28-32.5\\9x=-4.5\\x=-\frac{4.5}{9} \\x=-0.5[/tex]

Or , [tex]x=-\frac{1}{2}[/tex]

The solution for the set of equations is: [tex](-\frac{1}{2},\frac{13}{2})[/tex]

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