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The system of equations are (3/4)x + (4/5)y = 5/2 and (1/2)x - (9/10)y = - 11/2.

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Equation 1 : (3/4)x + (4/5)y = 5/2       ⇒    0.75x + 0.8y = 2.5.

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Equation 2 : (1/2)x - (9/10)y = - 11/2  ⇒    0.5x - 0.9y = - 5.5.

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Neither variable has a common coefficient.The coefficient  of the y - variables are 0.8 and 0.9 and their least common multiple is 0.72, so multiply each equation by the value  that will make the y - coefficient 0.72.

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To get two equations that contain opposite terms multiply the first equation by 0.9 and multiply the second equation by 0.8.

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Write the equations in column form and add the corresponding columns to eliminate y - variable.

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The resultant equation is 1.075x = - 2.15 ⇒ x = - 2.

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Substitute the value of x = - 2 in either of the original equations and solve for y.

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The second equation : 0.5x - 0.9y = - 5.5.

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0.5(- 2) - 0.9y = - 5.5

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- 1 - 0.9y = - 5.5

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- 0.9y = - 4.5

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y = 5.

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The solution (x, y) = (-2, 5).

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