Solve {rr}{p}&{3}{4}&{-2}{l}{1}{q}={l}{5}{0}

$$\left( \begin{array} { r r } { p } & { 3 } \\ { 4 } & { - 2 } \end{array} \right) \left( \begin{array} { l } { 1 } \\ { q } \end{array} \right) = \left( \begin{array} { l } { 5 } \\ { 0 } \end{array} \right)$$

Solve for p, q

$$p=-1$$

$$q=2$$

Solution Steps

Consider the second equation. Subtract 4 from both sides. Anything subtracted from zero gives its negation.

$$-2q=-4$$

Divide both sides by -2.

$$q=\frac{-4}{-2}$$

Divide -4 by -2 to get 2.

$$q=2$$

Consider the first equation. Insert the known values of variables into the equation.

$$p+3\times 2=5$$

Multiply 3 and 2 to get 6.

$$p+6=5$$

Subtract 6 from both sides.

$$p=5-6$$

Subtract 6 from 5 to get -1.

$$p=-1$$

The system is now solved.

$$p=-1 q=2$$