What is 5x+4y=7,2x-3y=4 ?

The solution to 5x+4y=7,2x-3y=4 is x= 37/23 ,y=-6/23

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5x+4y=7,2x-3y=4

5 x + 4 y = 7, 2 x - 3 y = 4

x = \frac{37}{23}, y = - \frac{6}{23}

Solution steps

[5 x + 4 y = 7 2 x - 3 y = 4]

Isolate

x

for

5 x + 4 y = 7 : x = \frac{7 - 4 y}{5}

Substitute

x = \frac{7 - 4 y}{5}

[2 \cdot \frac{7 - 4 y}{5} - 3 y = 4]

Simplify

[\frac{14 - 23 y}{5} = 4]

Isolate

y

for

\frac{14 - 23 y}{5} = 4 : y = - \frac{6}{23}

For

x = \frac{7 - 4 y}{5}

Substitute

y = - \frac{6}{23}

x = \frac{7 - 4 ( - \frac{6}{23} )}{5}

\frac{7 - 4 ( - \frac{6}{23} )}{5} = \frac{37}{23}

x = \frac{37}{23}

The solutions to the system of equations are:

x = \frac{37}{23}, y = - \frac{6}{23}

3 t + 4 c = 65, t + c = 18

x + y = 8, 2 x + y = 10

\frac{1}{( 7 x )} + \frac{1}{( 6 y )} = 3, \frac{1}{( 2 x )} - \frac{1}{( 3 y )} = 5

5 x + 2 y = 7, 7 x + 6 y = - 3

5 x + 7 y = 3, 3 x + 14 y = 6