What is ((x+1))/((y+1))=2,((2x+1))/((2y+1))= 1/3 ?

The solution to ((x+1))/((y+1))=2,((2x+1))/((2y+1))= 1/3 is

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((x+1))/((y+1))=2,((2x+1))/((2y+1))= 1/3

\frac{( x + 1 )}{( y + 1 )} = 2, \frac{( 2 x + 1 )}{( 2 y + 1 )} = \frac{1}{3}

(x = - \frac{3}{5}, y = - \frac{4}{5})

Solution steps

[\frac{( x + 1 )}{( y + 1 )} = 2 \frac{( 2 x + 1 )}{( 2 y + 1 )} = \frac{1}{3}]

Isolate

y

for

\frac{( x + 1 )}{( y + 1 )} = 2 : y = \frac{x + 1}{2} - 1

Plug the solutions

y = \frac{x + 1}{2} - 1

into

\frac{( 2 x + 1 )}{( 2 y + 1 )} = \frac{1}{3}

For

\frac{( 2 x + 1 )}{( 2 y + 1 )} = \frac{1}{3}

, subsitute

y

with

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

Plug the solutions

x = - \frac{3}{5}

into

\frac{( x + 1 )}{( y + 1 )} = 2

For

\frac{( x + 1 )}{( y + 1 )} = 2

, subsitute

x

with

- \frac{3}{5} : y = - \frac{4}{5}

Verify solutions by plugging them into the original equations

Therefore, the final solution for

\frac{( x + 1 )}{( y + 1 )} = 2, \frac{( 2 x + 1 )}{( 2 y + 1 )} = \frac{1}{3}

(x = - \frac{3}{5}, y = - \frac{4}{5})

(e) 5 x + 3 y = 11, 4 x - y = 2

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

19 x - 17 y = 55, 17 x - 19 y = 53

4 x - y = 10, 5 x - 2 y = 8

14 = 3 y + x, 20 = 2 y - 3 x

What is ((x+1))/((y+1))=2,((2x+1))/((2y+1))= 1/3 ?
The solution to ((x+1))/((y+1))=2,((2x+1))/((2y+1))= 1/3 is