Solve the System of Equations 4p-2t=6 8p+6t=12+2t

$4 p - 2 t = 6$ $8 p + 6 t = 12 + 2 t$

Solve for $p$ in $4 p - 2 t = 6$ .

Add $2 t$ to both sides of the equation.

$4 p = 6 + 2 t$

$8 p + 6 t = 12 + 2 t$

Divide each term in $4 p = 6 + 2 t$ by $4$ and simplify.

Divide each term in $4 p = 6 + 2 t$ by $4$ .

$\frac{4 p}{4} = \frac{6}{4} + \frac{2 t}{4}$

$8 p + 6 t = 12 + 2 t$

Simplify the left side.

Cancel the common factor of $4$ .

Cancel the common factor.

$\frac{4 p}{4} = \frac{6}{4} + \frac{2 t}{4}$

$8 p + 6 t = 12 + 2 t$

Divide $p$ by $1$ .

$p = \frac{6}{4} + \frac{2 t}{4}$

$8 p + 6 t = 12 + 2 t$

$p = \frac{6}{4} + \frac{2 t}{4}$

$8 p + 6 t = 12 + 2 t$

$p = \frac{6}{4} + \frac{2 t}{4}$

$8 p + 6 t = 12 + 2 t$

Simplify the right side.

Simplify each term.

Cancel the common factor of $6$ and $4$ .

Factor $2$ out of $6$ .

$p = \frac{2 (3)}{4} + \frac{2 t}{4}$

$8 p + 6 t = 12 + 2 t$

Cancel the common factors.

Factor $2$ out of $4$ .

$p = \frac{2 \cdot 3}{2 \cdot 2} + \frac{2 t}{4}$

$8 p + 6 t = 12 + 2 t$

Cancel the common factor.

$p = \frac{2 \cdot 3}{2 \cdot 2} + \frac{2 t}{4}$

$8 p + 6 t = 12 + 2 t$

Rewrite the expression.

$p = \frac{3}{2} + \frac{2 t}{4}$

$8 p + 6 t = 12 + 2 t$

$p = \frac{3}{2} + \frac{2 t}{4}$

$8 p + 6 t = 12 + 2 t$

$p = \frac{3}{2} + \frac{2 t}{4}$

$8 p + 6 t = 12 + 2 t$

Cancel the common factor of $2$ and $4$ .

Factor $2$ out of $2 t$ .

$p = \frac{3}{2} + \frac{2 (t)}{4}$

$8 p + 6 t = 12 + 2 t$

Cancel the common factors.

Factor $2$ out of $4$ .

$p = \frac{3}{2} + \frac{2 t}{2 \cdot 2}$

$8 p + 6 t = 12 + 2 t$

Cancel the common factor.

$p = \frac{3}{2} + \frac{2 t}{2 \cdot 2}$

$8 p + 6 t = 12 + 2 t$

Rewrite the expression.

$p = \frac{3}{2} + \frac{t}{2}$

$8 p + 6 t = 12 + 2 t$

$p = \frac{3}{2} + \frac{t}{2}$

$8 p + 6 t = 12 + 2 t$

$p = \frac{3}{2} + \frac{t}{2}$

$8 p + 6 t = 12 + 2 t$

$p = \frac{3}{2} + \frac{t}{2}$

$8 p + 6 t = 12 + 2 t$

$p = \frac{3}{2} + \frac{t}{2}$

$8 p + 6 t = 12 + 2 t$

$p = \frac{3}{2} + \frac{t}{2}$

$8 p + 6 t = 12 + 2 t$

$p = \frac{3}{2} + \frac{t}{2}$

$8 p + 6 t = 12 + 2 t$

Replace all occurrences of $p$ with $\frac{3}{2} + \frac{t}{2}$ in each equation.

Replace all occurrences of $p$ in $8 p + 6 t = 12 + 2 t$ with $\frac{3}{2} + \frac{t}{2}$ .

$8 (\frac{3}{2} + \frac{t}{2}) + 6 t = 12 + 2 t$

$p = \frac{3}{2} + \frac{t}{2}$

Simplify the left side.

Simplify $8 (\frac{3}{2} + \frac{t}{2}) + 6 t$ .

Simplify each term.

Apply the distributive property.

$8 (\frac{3}{2}) + 8 (\frac{t}{2}) + 6 t = 12 + 2 t$

$p = \frac{3}{2} + \frac{t}{2}$

Cancel the common factor of $2$ .

Factor $2$ out of $8$ .

$2 (4) (\frac{3}{2}) + 8 (\frac{t}{2}) + 6 t = 12 + 2 t$

$p = \frac{3}{2} + \frac{t}{2}$

Cancel the common factor.

$2 \cdot (4 (\frac{3}{2})) + 8 (\frac{t}{2}) + 6 t = 12 + 2 t$

$p = \frac{3}{2} + \frac{t}{2}$

Rewrite the expression.

$4 \cdot 3 + 8 (\frac{t}{2}) + 6 t = 12 + 2 t$

$p = \frac{3}{2} + \frac{t}{2}$

$4 \cdot 3 + 8 (\frac{t}{2}) + 6 t = 12 + 2 t$

$p = \frac{3}{2} + \frac{t}{2}$

Multiply $4$ by $3$ .

$12 + 8 (\frac{t}{2}) + 6 t = 12 + 2 t$

$p = \frac{3}{2} + \frac{t}{2}$

Cancel the common factor of $2$ .

Factor $2$ out of $8$ .

$12 + 2 (4) (\frac{t}{2}) + 6 t = 12 + 2 t$

$p = \frac{3}{2} + \frac{t}{2}$

Cancel the common factor.

$12 + 2 \cdot (4 (\frac{t}{2})) + 6 t = 12 + 2 t$

$p = \frac{3}{2} + \frac{t}{2}$

Rewrite the expression.

$12 + 4 t + 6 t = 12 + 2 t$

$p = \frac{3}{2} + \frac{t}{2}$

$12 + 4 t + 6 t = 12 + 2 t$

$p = \frac{3}{2} + \frac{t}{2}$

$12 + 4 t + 6 t = 12 + 2 t$

$p = \frac{3}{2} + \frac{t}{2}$

Add $4 t$ and $6 t$ .

$12 + 10 t = 12 + 2 t$

$p = \frac{3}{2} + \frac{t}{2}$

$12 + 10 t = 12 + 2 t$

$p = \frac{3}{2} + \frac{t}{2}$

$12 + 10 t = 12 + 2 t$

$p = \frac{3}{2} + \frac{t}{2}$

$12 + 10 t = 12 + 2 t$

$p = \frac{3}{2} + \frac{t}{2}$

Solve for $t$ in $12 + 10 t = 12 + 2 t$ .

Move all terms containing $t$ to the left side of the equation.

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

$12 + 10 t - 2 t = 12$

$p = \frac{3}{2} + \frac{t}{2}$

Subtract $2 t$ from $10 t$ .

$12 + 8 t = 12$

$p = \frac{3}{2} + \frac{t}{2}$

$12 + 8 t = 12$

$p = \frac{3}{2} + \frac{t}{2}$

Move all terms not containing $t$ to the right side of the equation.

Subtract $12$ from both sides of the equation.

$8 t = 12 - 12$

$p = \frac{3}{2} + \frac{t}{2}$

Subtract $12$ from $12$ .

$8 t = 0$

$p = \frac{3}{2} + \frac{t}{2}$

$8 t = 0$

$p = \frac{3}{2} + \frac{t}{2}$

Divide each term in $8 t = 0$ by $8$ and simplify.

Divide each term in $8 t = 0$ by $8$ .

$\frac{8 t}{8} = \frac{0}{8}$

$p = \frac{3}{2} + \frac{t}{2}$

Simplify the left side.

Cancel the common factor of $8$ .

Cancel the common factor.

$\frac{8 t}{8} = \frac{0}{8}$

$p = \frac{3}{2} + \frac{t}{2}$

Divide $t$ by $1$ .

$t = \frac{0}{8}$

$p = \frac{3}{2} + \frac{t}{2}$

$t = \frac{0}{8}$

$p = \frac{3}{2} + \frac{t}{2}$

$t = \frac{0}{8}$

$p = \frac{3}{2} + \frac{t}{2}$

Simplify the right side.

Divide $0$ by $8$ .

$t = 0$

$p = \frac{3}{2} + \frac{t}{2}$

$t = 0$

$p = \frac{3}{2} + \frac{t}{2}$

$t = 0$

$p = \frac{3}{2} + \frac{t}{2}$

$t = 0$

$p = \frac{3}{2} + \frac{t}{2}$

Replace all occurrences of $t$ with $0$ in each equation.

Replace all occurrences of $t$ in $p = \frac{3}{2} + \frac{t}{2}$ with $0$ .

$p = \frac{3}{2} + \frac{0}{2}$

$t = 0$

Simplify the right side.

Simplify $\frac{3}{2} + \frac{0}{2}$ .

Combine the numerators over the common denominator.

$p = \frac{3 + 0}{2}$

$t = 0$

Add $3$ and $0$ .

$p = \frac{3}{2}$

$t = 0$

$p = \frac{3}{2}$

$t = 0$

$p = \frac{3}{2}$

$t = 0$

$p = \frac{3}{2}$

$t = 0$

List all of the solutions.

$p = \frac{3}{2}, t = 0$

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