What is 4x+6y=2,6x+5y=1 ?

The solution to 4x+6y=2,6x+5y=1 is x=-1/4 ,y= 1/2

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4x+6y=2,6x+5y=1

4 x + 6 y = 2, 6 x + 5 y = 1

x = - \frac{1}{4}, y = \frac{1}{2}

Solution steps

[4 x + 6 y = 2 6 x + 5 y = 1]

Isolate

x

for

4 x + 6 y = 2 : x = \frac{1 - 3 y}{2}

Substitute

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

[6 \cdot \frac{1 - 3 y}{2} + 5 y = 1]

Simplify

[- 4 y + 3 = 1]

Isolate

y

for

- 4 y + 3 = 1 : y = \frac{1}{2}

For

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

Substitute

y = \frac{1}{2}

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

\frac{1 - 3 \cdot \frac{1}{2}}{2} = - \frac{1}{4}

x = - \frac{1}{4}

The solutions to the system of equations are:

x = - \frac{1}{4}, y = \frac{1}{2}

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

2 x + y = 5, x - y = 1

2 x - y = 6, x - y = 2

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

x + 2 y = 1, 2 x + 4 y = 3