What is 19x+3y=5,2x+y=(r+1) ?

The solution to 19x+3y=5,2x+y=(r+1) is x=(-3r+2)/(13),y=(19r+9)/(13)

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19x+3y=5,2x+y=(r+1)

19 x + 3 y = 5, 2 x + y = (r + 1)

x = \frac{- 3 r + 2}{13}, y = \frac{19 r + 9}{13}

Solution steps

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

Isolate

x

for

19 x + 3 y = 5 : x = \frac{5 - 3 y}{19}

Substitute

x = \frac{5 - 3 y}{19}

[2 \cdot \frac{5 - 3 y}{19} + y = (r + 1)]

Simplify

[\frac{10 + 13 y}{19} = r + 1]

Isolate

y

for

\frac{10 + 13 y}{19} = r + 1 : y = \frac{19 r + 9}{13}

For

x = \frac{5 - 3 y}{19}

Expressing

x

in terms of

r

x = \frac{5 - 3 \cdot \frac{19 r + 9}{13}}{19}

Simplify

\frac{5 - 3 \cdot \frac{19 r + 9}{13}}{19} : \frac{- 3 r + 2}{13}

x = \frac{- 3 r + 2}{13}

The solutions to the system of equations are:

x = \frac{- 3 r + 2}{13}, y = \frac{19 r + 9}{13}

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

4 x - y = 0, 3 x + 2 y = 12

\frac{x}{3} + y = 1, 2 x - 2 y = 0

x + 3 y = - 18, 4 x - y = - 7

4 x + 3 y = 11, 3 x + 4 y = 10

What is 19x+3y=5,2x+y=(r+1) ?
The solution to 19x+3y=5,2x+y=(r+1) is x=(-3r+2)/(13),y=(19r+9)/(13)