What is 2a+4b=12,3a+2b=100 ?

The solution to 2a+4b=12,3a+2b=100 is a=47,b=-41/2

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2a+4b=12,3a+2b=100

2 a + 4 b = 12, 3 a + 2 b = 100

a = 47, b = - \frac{41}{2}

Solution steps

[2 a + 4 b = 12 3 a + 2 b = 100]

Isolate

a

for

2 a + 4 b = 12 : a = 2 (- b + 3)

Substitute

a = 2 (- b + 3)

[3 \cdot 2 (- b + 3) + 2 b = 100]

Simplify

[- 4 b + 18 = 100]

Isolate

b

for

- 4 b + 18 = 100 : b = - \frac{41}{2}

For

a = 2 (- b + 3)

Substitute

b = - \frac{41}{2}

a = 2 (- (- \frac{41}{2}) + 3)

2 (- (- \frac{41}{2}) + 3) = 47

a = 47

The solutions to the system of equations are:

a = 47, b = - \frac{41}{2}

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

3 x + 2 y = 13, 2 x + 5 y = 5

2 x + 3 y = 9, 4 x + 6 y = 18

x_{1} = - 1, 0 y x_{2} = - 2

4 x + 5 y = 21, 4 x + 8 y = - 8