Solve {l}{kx-5=3x+2}{0.3(2x-4)=0.5(x+3)-2}

$$\left. \begin{array} { l } { k x - 5 = 3 x + 2 } \\ { 0.3 ( 2 x - 4 ) = 0.5 ( x + 3 ) - 2 } \end{array} \right.$$

Solve for k, x

$$x=7$$

$$k=4$$

Solution Steps

Consider the second equation. Use the distributive property to multiply 0.3 by 2x-4.

$$0.6x-1.2=0.5\left(x+3\right)-2$$

Use the distributive property to multiply 0.5 by x+3.

$$0.6x-1.2=0.5x+1.5-2$$

Subtract 2 from 1.5 to get -0.5.

$$0.6x-1.2=0.5x-0.5$$

Subtract 0.5x from both sides.

$$0.6x-1.2-0.5x=-0.5$$

Combine 0.6x and -0.5x to get 0.1x.

$$0.1x-1.2=-0.5$$

Add 1.2 to both sides.

$$0.1x=-0.5+1.2$$

Add -0.5 and 1.2 to get 0.7.

$$0.1x=0.7$$

Divide both sides by 0.1.

$$x=\frac{0.7}{0.1}$$

Expand \frac{0.7}{0.1} by multiplying both numerator and the denominator by 10. Anything divided by one gives itself.

$$x=7$$

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

$$k\times 7-5=3\times 7+2$$

Multiply 3 and 7 to get 21.

$$k\times 7-5=21+2$$

Add 21 and 2 to get 23.

$$k\times 7-5=23$$

Add 5 to both sides.

$$k\times 7=23+5$$

Add 23 and 5 to get 28.

$$k\times 7=28$$

Divide both sides by 7.

$$k=\frac{28}{7}$$

Divide 28 by 7 to get 4.

$$k=4$$

The system is now solved.

$$k=4 x=7$$