Solve {l}{dx:(i)-3(4x+9)=21}{(7x-5)-4(2+5x)=1}

$$\left. \begin{array} { l } { d x : ( i ) - 3 ( 4 x + 9 ) = 21 } \\ { ( 7 x - 5 ) - 4 ( 2 + 5 x ) = 1 } \end{array} \right.$$

Solve for d, x

$$x = -\frac{14}{13} = -1\frac{1}{13} \approx -1.076923077$$

$$d=-\frac{228}{7}i\approx -32.571428571i$$

Solution Steps

Consider the second equation. Use the distributive property to multiply -4 by 2+5x.

$$7x-5-8-20x=1$$

Subtract 8 from -5 to get -13.

$$7x-13-20x=1$$

Combine 7x and -20x to get -13x.

$$-13x-13=1$$

Add 13 to both sides.

$$-13x=1+13$$

Add 1 and 13 to get 14.

$$-13x=14$$

Divide both sides by -13.

$$x=-\frac{14}{13}$$

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

$$\frac{d\left(-\frac{14}{13}\right)}{i}-3\left(4\left(-\frac{14}{13}\right)+9\right)=21$$

Divide d\left(-\frac{14}{13}\right) by i to get d\times \left(\frac{14}{13}i\right).

$$d\times \left(\frac{14}{13}i\right)-3\left(4\left(-\frac{14}{13}\right)+9\right)=21$$

Multiply 4 and -\frac{14}{13} to get -\frac{56}{13}.

$$d\times \left(\frac{14}{13}i\right)-3\left(-\frac{56}{13}+9\right)=21$$

Add -\frac{56}{13} and 9 to get \frac{61}{13}.

$$d\times \left(\frac{14}{13}i\right)-3\times \frac{61}{13}=21$$

Multiply -3 and \frac{61}{13} to get -\frac{183}{13}.

$$d\times \left(\frac{14}{13}i\right)-\frac{183}{13}=21$$

Add \frac{183}{13} to both sides.

$$d\times \left(\frac{14}{13}i\right)=21+\frac{183}{13}$$

Add 21 and \frac{183}{13} to get \frac{456}{13}.

$$d\times \left(\frac{14}{13}i\right)=\frac{456}{13}$$

Divide both sides by \frac{14}{13}i.

$$d=\frac{\frac{456}{13}}{\frac{14}{13}i}$$

Multiply both numerator and denominator of \frac{\frac{456}{13}}{\frac{14}{13}i} by imaginary unit i.

$$d=\frac{\frac{456}{13}i}{-\frac{14}{13}}$$

Divide \frac{456}{13}i by -\frac{14}{13} to get -\frac{228}{7}i.

$$d=-\frac{228}{7}i$$

The system is now solved.

$$d=-\frac{228}{7}i x=-\frac{14}{13}$$