What is 3a+5b=2,6a+5b=22 ?

The solution to 3a+5b=2,6a+5b=22 is a= 20/3 ,b=-18/5

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3a+5b=2,6a+5b=22

3 a + 5 b = 2, 6 a + 5 b = 22

a = \frac{20}{3}, b = - \frac{18}{5}

Solution steps

[3 a + 5 b = 2 6 a + 5 b = 22]

Isolate

a

for

3 a + 5 b = 2 : a = \frac{2 - 5 b}{3}

Substitute

a = \frac{2 - 5 b}{3}

[6 \cdot \frac{2 - 5 b}{3} + 5 b = 22]

Simplify

[- 5 b + 4 = 22]

Isolate

b

for

- 5 b + 4 = 22 : b = - \frac{18}{5}

For

a = \frac{2 - 5 b}{3}

Substitute

b = - \frac{18}{5}

a = \frac{2 - 5 ( - \frac{18}{5} )}{3}

\frac{2 - 5 ( - \frac{18}{5} )}{3} = \frac{20}{3}

a = \frac{20}{3}

The solutions to the system of equations are:

a = \frac{20}{3}, b = - \frac{18}{5}

x + 3 y = - 8, 4 x - 5 y = 2

x - 3 y - 3 = 3, x - 9 y - 2 = 0

2 x + y = - 10, x - 3 y = 2

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

4 x + 2 y = 8, 3 x - y = 1