What is 6a+2b=3,7a+7b=1 ?

The solution to 6a+2b=3,7a+7b=1 is a= 19/28 ,b=-15/28

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6a+2b=3,7a+7b=1

6 a + 2 b = 3, 7 a + 7 b = 1

a = \frac{19}{28}, b = - \frac{15}{28}

Solution steps

[6 a + 2 b = 3 7 a + 7 b = 1]

Isolate

a

for

6 a + 2 b = 3 : a = \frac{3 - 2 b}{6}

Substitute

a = \frac{3 - 2 b}{6}

[7 \cdot \frac{3 - 2 b}{6} + 7 b = 1]

Simplify

[\frac{21 + 28 b}{6} = 1]

Isolate

b

for

\frac{21 + 28 b}{6} = 1 : b = - \frac{15}{28}

For

a = \frac{3 - 2 b}{6}

Substitute

b = - \frac{15}{28}

a = \frac{3 - 2 ( - \frac{15}{28} )}{6}

\frac{3 - 2 ( - \frac{15}{28} )}{6} = \frac{19}{28}

a = \frac{19}{28}

The solutions to the system of equations are:

a = \frac{19}{28}, b = - \frac{15}{28}

2 x + y = 12, 3 x - 5 y = 18

x + y - z = 1, z + x - y = 3, z - x + y = 7

4 x - 3 y = 9, 3 x - 4 y = 5

8 x - 5 y + 40 = 7, x - 2 y = 0

\frac{7}{x} - \frac{15}{y} = 9, \cdot \frac{11}{x} - \frac{8}{y} = - 17