What is 3x+4y=2,4x+3y=4 ?

The solution to 3x+4y=2,4x+3y=4 is x= 10/7 ,y=-4/7

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3x+4y=2,4x+3y=4

3 x + 4 y = 2, 4 x + 3 y = 4

x = \frac{10}{7}, y = - \frac{4}{7}

Solution steps

[3 x + 4 y = 2 4 x + 3 y = 4]

Isolate

x

for

3 x + 4 y = 2 : x = \frac{2 - 4 y}{3}

Substitute

x = \frac{2 - 4 y}{3}

[4 \cdot \frac{2 - 4 y}{3} + 3 y = 4]

Simplify

[\frac{8 - 7 y}{3} = 4]

Isolate

y

for

\frac{8 - 7 y}{3} = 4 : y = - \frac{4}{7}

For

x = \frac{2 - 4 y}{3}

Substitute

y = - \frac{4}{7}

x = \frac{2 - 4 ( - \frac{4}{7} )}{3}

\frac{2 - 4 ( - \frac{4}{7} )}{3} = \frac{10}{7}

x = \frac{10}{7}

The solutions to the system of equations are:

x = \frac{10}{7}, y = - \frac{4}{7}

x + y = 1, 2 x - y = 2

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

x + y = 10, 2 x - y = 20

(d) (3 \frac{y}{2}) - (5 \frac{x}{3}) = - 2, (\frac{y}{3}) + (\frac{x}{3}) = \frac{13}{6}

4 n - 2 m - 3 r = 1, m + 3 n + 5 r = - 4, 3 m - 5 n + r = 0