What is 7x+5y=2,7x=y-3 ?

The solution to 7x+5y=2,7x=y-3 is x=-13/42 ,y= 5/6

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

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

x = - \frac{13}{42}, y = \frac{5}{6}

Solution steps

[7 x + 5 y = 2 7 x = y - 3]

Isolate

x

for

7 x + 5 y = 2 : x = \frac{2 - 5 y}{7}

Substitute

x = \frac{2 - 5 y}{7}

[7 \cdot \frac{2 - 5 y}{7} = y - 3]

Simplify

[2 - 5 y = y - 3]

Isolate

y

for

2 - 5 y = y - 3 : y = \frac{5}{6}

For

x = \frac{2 - 5 y}{7}

Substitute

y = \frac{5}{6}

x = \frac{2 - 5 \cdot \frac{5}{6}}{7}

\frac{2 - 5 \cdot \frac{5}{6}}{7} = - \frac{13}{42}

x = - \frac{13}{42}

The solutions to the system of equations are:

x = - \frac{13}{42}, y = \frac{5}{6}

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4 x - 3 y = - 10, 6 x + 9 y = 12