What is 2x+3r=2,2x-3y=0 ?

The solution to 2x+3r=2,2x-3y=0 is r=-(3y-2)/3 ,x=(3y)/2

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2x+3r=2,2x-3y=0

2 x + 3 r = 2, 2 x - 3 y = 0

r = - \frac{3 y - 2}{3}, x = \frac{3 y}{2}

Solution steps

[2 x + 3 r = 2 2 x - 3 y = 0]

Isolate

x

for

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

Substitute

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

[2 \cdot \frac{2 - 3 r}{2} - 3 y = 0]

Simplify

[2 - 3 r - 3 y = 0]

Isolate

r

for

2 - 3 r - 3 y = 0 : r = - \frac{3 y - 2}{3}

For

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

Expressing

x

in terms of

y

x = \frac{2 - 3 ( - \frac{3 y - 2}{3} )}{2}

Simplify

\frac{2 - 3 ( - \frac{3 y - 2}{3} )}{2} : \frac{3 y}{2}

x = \frac{3 y}{2}

The solutions to the system of equations are:

r = - \frac{3 y - 2}{3}, x = \frac{3 y}{2}

3 x + 2 y = 4, 2 x - 3 y = 7

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

7 x + 4 y = 26, 3 x - 4 y = 4

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

5 x - 4 y = - 1, 0 y = 2 x - 5

What is 2x+3r=2,2x-3y=0 ?
The solution to 2x+3r=2,2x-3y=0 is r=-(3y-2)/3 ,x=(3y)/2