Solve the set of equations 3x - 8y = 10 and 2x + 3y = 6

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You may use matrices to solve the system, hence, you need to create the matrix of coefficients of variables, such that:

A = ((3,-8),(2,3))

You need to evaluate the determinant of the matrix A, such that:

`det A = [(3,-8),(2,3)]` => `det A = 9 + 16 => detA =...

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You may use matrices to solve the system, hence, you need to create the matrix of coefficients of variables, such that:

A = ((3,-8),(2,3))

You need to evaluate the determinant of the matrix A, such that:

`det A = [(3,-8),(2,3)]` => `det A = 9 + 16 => detA = 25`

You need to use Cramer's formulas to evaluate x and y, such that:

`x = (Delta_x)/(det A); y = (Delta_y)/(det A);`

`Delta_x = [(10,-8),(6,3)]` => `Delta_x =30 + 48 = 78`

`x = 78/25`

`Delta_y = [(3,10),(2,6)]` =>` Delta_y = 18 - 20 = -2`

`y = -2/25`

Hence, evaluating the solution to the system of equations, using Cramer's formulas, yields `x = 78/25, y = -2/25` .

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The system of equations consisting of 3x - 8y = 10 and 2x + 3y = 6 has to be solved for x and y.

3x - 8y = 10

=> 3x = 10 + 8y

=> x = 10/3 + (8y)/3

Substitute this for x in 2x + 3y = 6

=> 2*(10/3 + (8y)/3) + 3y = 6

=> 20/3 + (16*y)/3 + 3y = 6

=> (25y)/3 = 6 - 20/3

=> 25y = -2

=> y = -2/25

x = 10/3 + (8y)/3 = 10/3 - 16/75 = 78/25

The solution of the given set of equations is x = 78/25 and y = -2/25

Approved by eNotes Editorial Team