3, left parenthesis, r, plus, 2, s, right parenthesis, equals, 2, t, minus, 4

Solve for r

r=\frac{2\left(-3s+t-2\right)}{3}

Solve for s

s=\frac{t}{3}-\frac{r}{2}-\frac{2}{3}

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3r+6s=2t-4

Use the distributive property to multiply 3 by r+2s.

3r=2t-4-6s

Subtract 6s from both sides.

3r=-6s+2t-4

The equation is in standard form.

\frac{3r}{3}=\frac{-6s+2t-4}{3}

Divide both sides by 3.

r=\frac{-6s+2t-4}{3}

Dividing by 3 undoes the multiplication by 3.

r=\frac{2t}{3}-2s-\frac{4}{3}

Divide -4+2t-6s by 3.

3r+6s=2t-4

Use the distributive property to multiply 3 by r+2s.

6s=2t-4-3r

Subtract 3r from both sides.

6s=-3r+2t-4

The equation is in standard form.

\frac{6s}{6}=\frac{-3r+2t-4}{6}

Divide both sides by 6.

s=\frac{-3r+2t-4}{6}

Dividing by 6 undoes the multiplication by 6.

s=\frac{t}{3}-\frac{r}{2}-\frac{2}{3}

Divide 2t-4-3r by 6.