Solve {l}{1.5x-35y=-5}{-1.2y+2.5y=1}

$$\left\{ \begin{array} { l } { 1.5 x - 35 y = - 5 } \\ { - 1.2 y + 2.5 y = 1 } \end{array} \right.$$

Solve for x, y

$$x = \frac{190}{13} = 14\frac{8}{13} \approx 14.615384615$$

$$y=\frac{10}{13}\approx 0.769230769$$

Solution Steps

Consider the second equation. Combine -1.2y and 2.5y to get 1.3y.

$$1.3y=1$$

Divide both sides by 1.3.

$$y=\frac{1}{1.3}$$

Expand \frac{1}{1.3} by multiplying both numerator and the denominator by 10.

$$y=\frac{10}{13}$$

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

$$1.5x-35\times \frac{10}{13}=-5$$

Multiply -35 and \frac{10}{13} to get -\frac{350}{13}.

$$1.5x-\frac{350}{13}=-5$$

Add \frac{350}{13} to both sides.

$$1.5x=-5+\frac{350}{13}$$

Add -5 and \frac{350}{13} to get \frac{285}{13}.

$$1.5x=\frac{285}{13}$$

Divide both sides by 1.5.

$$x=\frac{\frac{285}{13}}{1.5}$$

Express \frac{\frac{285}{13}}{1.5} as a single fraction.

$$x=\frac{285}{13\times 1.5}$$

Multiply 13 and 1.5 to get 19.5.

$$x=\frac{285}{19.5}$$

Expand \frac{285}{19.5} by multiplying both numerator and the denominator by 10.

$$x=\frac{2850}{195}$$

Reduce the fraction \frac{2850}{195} to lowest terms by extracting and canceling out 15.

$$x=\frac{190}{13}$$

The system is now solved.

$$x=\frac{190}{13} y=\frac{10}{13}$$