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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 drop-down menu. Find the solution set for the system of equations. 9x + 5y = 28 5x + 9y = 56 The solution set for the system class=

Answer :

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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