Solve the System of Equations h+2k=3 3h+6k=9

$h + 2 k = 3$ $3 h + 6 k = 9$

Step 1

Subtract $2 k$ from both sides of the equation.

$h = 3 - 2 k$

$3 h + 6 k = 9$

Step 2

Replace all occurrences of $h$ with $3 - 2 k$ in each equation.

Replace all occurrences of $h$ in $3 h + 6 k = 9$ with $3 - 2 k$ .

$3 (3 - 2 k) + 6 k = 9$

$h = 3 - 2 k$

Simplify the left side.

Simplify $3 (3 - 2 k) + 6 k$ .

Simplify each term.

Apply the distributive property.

$3 \cdot 3 + 3 (- 2 k) + 6 k = 9$

$h = 3 - 2 k$

Multiply $3$ by $3$ .

$9 + 3 (- 2 k) + 6 k = 9$

$h = 3 - 2 k$

Multiply $- 2$ by $3$ .

$9 - 6 k + 6 k = 9$

$h = 3 - 2 k$

$9 - 6 k + 6 k = 9$

$h = 3 - 2 k$

Combine the opposite terms in $9 - 6 k + 6 k$ .

Add $- 6 k$ and $6 k$ .

$9 + 0 = 9$

$h = 3 - 2 k$

Add $9$ and $0$ .

$9 = 9$

$h = 3 - 2 k$

$9 = 9$

$h = 3 - 2 k$

$9 = 9$

$h = 3 - 2 k$

$9 = 9$

$h = 3 - 2 k$

$9 = 9$

$h = 3 - 2 k$

Step 3

Remove any equations from the system that are always true.

$h = 3 - 2 k$