What is 2x+3y=3,6y-6x=1 ?

The solution to 2x+3y=3,6y-6x=1 is x= 1/2 ,y= 2/3

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2x+3y=3,6y-6x=1

2 x + 3 y = 3, 6 y - 6 x = 1

x = \frac{1}{2}, y = \frac{2}{3}

Solution steps

[2 x + 3 y = 3 6 y - 6 x = 1]

Isolate

x

for

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

Substitute

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

[6 y - 6 \cdot \frac{3 - 3 y}{2} = 1]

Simplify

[15 y - 9 = 1]

Isolate

y

for

15 y - 9 = 1 : y = \frac{2}{3}

For

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

Substitute

y = \frac{2}{3}

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

\frac{3 - 3 \cdot \frac{2}{3}}{2} = \frac{1}{2}

x = \frac{1}{2}

The solutions to the system of equations are:

x = \frac{1}{2}, y = \frac{2}{3}

3 x + 2 y = 9, 5 x + 3 y = 14

4 x + 3 y = 7, 5 x - 4 y = 32

x + 3 y = 5, 2 x - 3 y = - 8

7 x - 4 y = 5, 9 x + 8 y = 13

3 x + 2 y = - 12, 2 x - 3 y = 5