What is 2x-3y=5,x+4y=1 ?

The solution to 2x-3y=5,x+4y=1 is x= 23/11 ,y=-3/11

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2x-3y=5,x+4y=1

2 x - 3 y = 5, x + 4 y = 1

x = \frac{23}{11}, y = - \frac{3}{11}

Solution steps

[2 x - 3 y = 5 x + 4 y = 1]

Isolate

x

for

2 x - 3 y = 5 : x = \frac{5 + 3 y}{2}

Substitute

x = \frac{5 + 3 y}{2}

[\frac{5 + 3 y}{2} + 4 y = 1]

Simplify

[\frac{5 + 11 y}{2} = 1]

Isolate

y

for

\frac{5 + 11 y}{2} = 1 : y = - \frac{3}{11}

For

x = \frac{5 + 3 y}{2}

Substitute

y = - \frac{3}{11}

x = \frac{5 + 3 ( - \frac{3}{11} )}{2}

\frac{5 + 3 ( - \frac{3}{11} )}{2} = \frac{23}{11}

x = \frac{23}{11}

The solutions to the system of equations are:

x = \frac{23}{11}, y = - \frac{3}{11}

a = 2, b = 3, c = 4

x - y = 2, 3 x - 2 y = 1

a + b + c = 0, a - 3 b + c = 1, - 2 a - 1 c = - 1

2 x - 5 y = 14, 3 x + y = 4

x = 6, y = 3