Solve the systems algebraically: `5x+7y+2=9y-4x+6` `21/2x-4/3y-11/4=3/2x+2/3y+5/4`5X+7Y+2=9Y-4X+6 21/2X-4/3Y-11/4=3/2X+2/3Y+5/4

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lemjay eNotes educator| Certified Educator

Simplify the given equations.

For the first equation, move the terms with variable to the left side. And the terms without variable to the right side.

          `5x+7y+2=9y-4x+6`

`5x+7y-9y+4x=6-2`

               `9x-2y=4`                 (Let this be EQ1.) 

For the second equation, to cancel the denominators, multiply both sides by the LCD.

          `21/2x-4/3y-11/4=3/2x+2/3y+5/4`

 `12*(21/2x-4/3y-11/4)=(3/2x+2/3y+5/4)*12`

`6*21x-4*4y-3*11=6*3x+4*2y+3*5`

      `126x-16y-33=18x+8y+15`

Bring together the terms with variable on the left side of the equation and the term without variable on the right side.

`126x-16y-18x-8y=15+33`

               `108x -24y=48`

To simplify further, divide both sides by the GCF of the three terms.

                `(108x-24y)/12=48/12`

                 `9x-2y=4`                (Let this be EQ2.)

Since EQ1 and EQ2 are the same, this means that their graph coincide with each other. So the resulting graph of the two equations result to same line.

Therefore, the given system of equations has infinite solutions.

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