What is 2x+3y=2,-6x+12y=1 ?

The solution to 2x+3y=2,-6x+12y=1 is x= 1/2 ,y= 1/3

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2x+3y=2,-6x+12y=1

2 x + 3 y = 2, - 6 x + 12 y = 1

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

Solution steps

[2 x + 3 y = 2 - 6 x + 12 y = 1]

Isolate

x

for

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

Substitute

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

[- 6 \cdot \frac{2 - 3 y}{2} + 12 y = 1]

Simplify

[21 y - 6 = 1]

Isolate

y

for

21 y - 6 = 1 : y = \frac{1}{3}

For

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

Substitute

y = \frac{1}{3}

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

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

x = \frac{1}{2}

The solutions to the system of equations are:

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

4 y + 3 x = 8, 8 x - 9 y = - 77

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

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

x + 3 y = 2, 2 x + y = 4

7 x + 4 y = 30, 3 y + 2 y = 14