What is 9x+16y=7,-3x+4y=0 ?

The solution to 9x+16y=7,-3x+4y=0 is x= 1/3 ,y= 1/4

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9x+16y=7,-3x+4y=0

9 x + 16 y = 7, - 3 x + 4 y = 0

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

Solution steps

[9 x + 16 y = 7 - 3 x + 4 y = 0]

Isolate

x

for

9 x + 16 y = 7 : x = \frac{7 - 16 y}{9}

Substitute

x = \frac{7 - 16 y}{9}

[- 3 \cdot \frac{7 - 16 y}{9} + 4 y = 0]

Simplify

[\frac{- 7 + 28 y}{3} = 0]

Isolate

y

for

\frac{- 7 + 28 y}{3} = 0 : y = \frac{1}{4}

For

x = \frac{7 - 16 y}{9}

Substitute

y = \frac{1}{4}

x = \frac{7 - 16 \cdot \frac{1}{4}}{9}

\frac{7 - 16 \cdot \frac{1}{4}}{9} = \frac{1}{3}

x = \frac{1}{3}

The solutions to the system of equations are:

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

23 x + 31 y = 77, 31 x + 23 y = 85

2 x - 5 y = 1, x - 10 y = - 22

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

2 x + 3 y = 5, 4 x + 6 y - 10 = 0

\frac{a}{b} = \frac{9}{11}, a + b = 800