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

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

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

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

x = - \frac{1}{3}, y = \frac{4}{3}

Solution steps

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

Isolate

x

for

5 x + 2 y = 1 : x = \frac{1 - 2 y}{5}

Substitute

x = \frac{1 - 2 y}{5}

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

Simplify

[\frac{- 3 + 21 y}{5} = 5]

Isolate

y

for

\frac{- 3 + 21 y}{5} = 5 : y = \frac{4}{3}

For

x = \frac{1 - 2 y}{5}

Substitute

y = \frac{4}{3}

x = \frac{1 - 2 \cdot \frac{4}{3}}{5}

\frac{1 - 2 \cdot \frac{4}{3}}{5} = - \frac{1}{3}

x = - \frac{1}{3}

The solutions to the system of equations are:

x = - \frac{1}{3}, y = \frac{4}{3}

- 4 x + 2 y = - 60, - 2 x - 6 y = 12

3 x - 2 y = 12, 3 x + 2 y = 0

7 x - 2 y = 4, 2 x + y = 9

152 x - 378 y = - 74, - 378 x + 152 y = - 604

x + 2 y = 10, 2 x - y = 5