What is 2x+5y=3,(k+1)x+2(k+2)y=2k ?

The solution to 2x+5y=3,(k+1)x+2(k+2)y=2k is x=4,y=-1,\quad k\ne 3

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2x+5y=3,(k+1)x+2(k+2)y=2k

2 x + 5 y = 3, (k + 1) x + 2 (k + 2) y = 2 k

x = 4, y = - 1, k \neq = 3

Solution steps

[2 x + 5 y = 3 (k + 1) x + 2 (k + 2) y = 2 k]

Isolate

x

for

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

Substitute

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

[(k + 1) \frac{3 - 5 y}{2} + 2 (k + 2) y = 2 k]

Simplify

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

Isolate

y

for

\frac{- k y + 3 y + 3 k + 3}{2} = 2 k : y = - 1; k \neq = 3

For

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

Substitute

y = - 1

x = \frac{3 - 5 ( - 1 )}{2}

\frac{3 - 5 ( - 1 )}{2} = 4

x = 4

The solutions to the system of equations are:

x = 4, y = - 1, k \neq = 3

3 x - 2 y = - 2, 5 x + 8 y = - 60

x - y + 4 z = 5, 2 x + z = 0, x + 3 y + z = - 15

3 x - 4 y = 4, 2 x - y = 3

55 x + 52 y = 21, 752 x + 55 y = 217

x - 3 y = - 2 x + 9, y = 4

What is 2x+5y=3,(k+1)x+2(k+2)y=2k ?
The solution to 2x+5y=3,(k+1)x+2(k+2)y=2k is x=4,y=-1,\quad k\ne 3