What is 3x+2y=6,2x+3y=5 ?

The solution to 3x+2y=6,2x+3y=5 is x= 8/5 ,y= 3/5

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

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

x = \frac{8}{5}, y = \frac{3}{5}

Solution steps

[3 x + 2 y = 6 2 x + 3 y = 5]

Isolate

x

for

3 x + 2 y = 6 : x = \frac{6 - 2 y}{3}

Substitute

x = \frac{6 - 2 y}{3}

[2 \cdot \frac{6 - 2 y}{3} + 3 y = 5]

Simplify

[\frac{12 + 5 y}{3} = 5]

Isolate

y

for

\frac{12 + 5 y}{3} = 5 : y = \frac{3}{5}

For

x = \frac{6 - 2 y}{3}

Substitute

y = \frac{3}{5}

x = \frac{6 - 2 \cdot \frac{3}{5}}{3}

\frac{6 - 2 \cdot \frac{3}{5}}{3} = \frac{8}{5}

x = \frac{8}{5}

The solutions to the system of equations are:

x = \frac{8}{5}, y = \frac{3}{5}

4 x + 5 y = - 9, 3 x + 4 y = - 8

x + y = 1, 1 x - y = 3

- 2 x + 5 y = 13, 16 x + 3 y = 25

x + 2 y = 1, - 3 x - y = 2

5 x - y = 6, x + 3 y = 10