Solve {l}{-7(1-4m)=13(2m-3)}{9(11-k)=3(3k-9)}

$$\left. \begin{array} { l } { - 7 ( 1 - 4 m ) = 13 ( 2 m - 3 ) } \\ { 9 ( 11 - k ) = 3 ( 3 k - 9 ) } \end{array} \right.$$

Solve for m, k

$$m=-16$$

$$k=7$$

Solution Steps

Consider the first equation. Use the distributive property to multiply -7 by 1-4m.

$$-7+28m=13\left(2m-3\right)$$

Use the distributive property to multiply 13 by 2m-3.

$$-7+28m=26m-39$$

Subtract 26m from both sides.

$$-7+28m-26m=-39$$

Combine 28m and -26m to get 2m.

$$-7+2m=-39$$

Add 7 to both sides.

$$2m=-39+7$$

Add -39 and 7 to get -32.

$$2m=-32$$

Divide both sides by 2.

$$m=\frac{-32}{2}$$

Divide -32 by 2 to get -16.

$$m=-16$$

Consider the second equation. Use the distributive property to multiply 9 by 11-k.

$$99-9k=3\left(3k-9\right)$$

Use the distributive property to multiply 3 by 3k-9.

$$99-9k=9k-27$$

Subtract 9k from both sides.

$$99-9k-9k=-27$$

Combine -9k and -9k to get -18k.

$$99-18k=-27$$

Subtract 99 from both sides.

$$-18k=-27-99$$

Subtract 99 from -27 to get -126.

$$-18k=-126$$

Divide both sides by -18.

$$k=\frac{-126}{-18}$$

Divide -126 by -18 to get 7.

$$k=7$$

The system is now solved.

$$m=-16 k=7$$