Solve {l}{75*4+30*x/5=3.120}{100x+300y+520=3120}

$$\left.\begin{array} { l } { 75 \times 4 + 30 \cdot \frac { x } { 5 } = 3.120 } \\ { 100 x + 300 y + 520 = 3120 } \end{array} \right\}$$

Solve for x, y

$$x=-49.48$$

$$y=25.16$$

Solution Steps

Consider the first equation. Multiply both sides of the equation by 5.

$$375\times 4+30x=15.6$$

Multiply 375 and 4 to get 1500.

$$1500+30x=15.6$$

Subtract 1500 from both sides.

$$30x=15.6-1500$$

Subtract 1500 from 15.6 to get -1484.4.

$$30x=-1484.4$$

Divide both sides by 30.

$$x=\frac{-1484.4}{30}$$

Expand \frac{-1484.4}{30} by multiplying both numerator and the denominator by 10.

$$x=\frac{-14844}{300}$$

Reduce the fraction \frac{-14844}{300} to lowest terms by extracting and canceling out 12.

$$x=-\frac{1237}{25}$$

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

$$100\left(-\frac{1237}{25}\right)+300y+520=3120$$

Multiply 100 and -\frac{1237}{25} to get -4948.

$$-4948+300y+520=3120$$

Add -4948 and 520 to get -4428.

$$-4428+300y=3120$$

Add 4428 to both sides.

$$300y=3120+4428$$

Add 3120 and 4428 to get 7548.

$$300y=7548$$

Divide both sides by 300.

$$y=\frac{7548}{300}$$

Reduce the fraction \frac{7548}{300} to lowest terms by extracting and canceling out 12.

$$y=\frac{629}{25}$$

The system is now solved.

$$x=-\frac{1237}{25} y=\frac{629}{25}$$