What is 2x+3y=1,6x+5y=1 ?

The solution to 2x+3y=1,6x+5y=1 is x=-1/4 ,y= 1/2

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2x+3y=1,6x+5y=1

2 x + 3 y = 1, 6 x + 5 y = 1

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

Solution steps

[2 x + 3 y = 1 6 x + 5 y = 1]

Isolate

x

for

2 x + 3 y = 1 : 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}

- x^{2} x = 0, y = 6, y = 1, y = 5

2 x + 5 y = 3, (k + 1) x + 2 (k + 2) y = 2 k

3 x - 2 y = - 2, 5 x + 8 y = - 60

x - y + 4 z = 5, 2 x + z = 0, x + 3 y + z = - 15

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