Solve {l}{3{2x-6[5k-3(2x-5)-8]+35}=4(2x-1)-1}{3{2x-6[5x-6x+15-8]+35}=8x-4-1}

$$\left. \begin{array} { l } { 3 \{ 2 x - 6 [ 5 k - 3 ( 2 x - 5 ) - 8 ] + 35 \} = 4 ( 2 x - 1 ) - 1 } \\ { 3 \{ 2 x - 6 [ 5 x - 6 x + 15 - 8 ] + 35 \} = 8 x - 4 - 1 } \end{array} \right.$$

Solve for x, k

$$x=1$$

$$k=1$$

Solution Steps

Consider the second equation. Combine 5x and -6x to get -x.

$$3\left(2x-6\left(-x+15-8\right)+35\right)=8x-4-1$$

Subtract 8 from 15 to get 7.

$$3\left(2x-6\left(-x+7\right)+35\right)=8x-4-1$$

Use the distributive property to multiply -6 by -x+7.

$$3\left(2x+6x-42+35\right)=8x-4-1$$

Combine 2x and 6x to get 8x.

$$3\left(8x-42+35\right)=8x-4-1$$

Add -42 and 35 to get -7.

$$3\left(8x-7\right)=8x-4-1$$

Use the distributive property to multiply 3 by 8x-7.

$$24x-21=8x-4-1$$

Subtract 1 from -4 to get -5.

$$24x-21=8x-5$$

Subtract 8x from both sides.

$$24x-21-8x=-5$$

Combine 24x and -8x to get 16x.

$$16x-21=-5$$

Add 21 to both sides.

$$16x=-5+21$$

Add -5 and 21 to get 16.

$$16x=16$$

Divide both sides by 16.

$$x=\frac{16}{16}$$

Divide 16 by 16 to get 1.

$$x=1$$

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

$$3\left(2\times 1-6\left(5k-3\left(2-5\right)-8\right)+35\right)=4\left(2\times 1-1\right)-1$$

Multiply 2 and 1 to get 2.

$$3\left(2-6\left(5k-3\left(2-5\right)-8\right)+35\right)=4\left(2\times 1-1\right)-1$$

Subtract 5 from 2 to get -3.

$$3\left(2-6\left(5k-3\left(-3\right)-8\right)+35\right)=4\left(2\times 1-1\right)-1$$

Multiply -3 and -3 to get 9.

$$3\left(2-6\left(5k+9-8\right)+35\right)=4\left(2\times 1-1\right)-1$$

Subtract 8 from 9 to get 1.

$$3\left(2-6\left(5k+1\right)+35\right)=4\left(2\times 1-1\right)-1$$

Use the distributive property to multiply -6 by 5k+1.

$$3\left(2-30k-6+35\right)=4\left(2\times 1-1\right)-1$$

Subtract 6 from 2 to get -4.

$$3\left(-4-30k+35\right)=4\left(2\times 1-1\right)-1$$

Add -4 and 35 to get 31.

$$3\left(31-30k\right)=4\left(2\times 1-1\right)-1$$

Use the distributive property to multiply 3 by 31-30k.

$$93-90k=4\left(2\times 1-1\right)-1$$

Multiply 2 and 1 to get 2.

$$93-90k=4\left(2-1\right)-1$$

Subtract 1 from 2 to get 1.

$$93-90k=4\times 1-1$$

Multiply 4 and 1 to get 4.

$$93-90k=4-1$$

Subtract 1 from 4 to get 3.

$$93-90k=3$$

Subtract 93 from both sides.

$$-90k=3-93$$

Subtract 93 from 3 to get -90.

$$-90k=-90$$

Divide both sides by -90.

$$k=\frac{-90}{-90}$$

Divide -90 by -90 to get 1.

$$k=1$$

The system is now solved.

$$x=1 k=1$$