Solve {l}{2x-5(1-3x)=1-3(1-2x)}{2x-5+5y=1-3+6x}

$$\left. \begin{array} { l } { 2 x - 5 ( 1 - 3 x ) = 1 - 3 ( 1 - 2 x ) } \\ { 2 x - 5 + 5 y = 1 - 3 + 6 x } \end{array} \right.$$

Solve for x, y

$$x=\frac{3}{11}\approx 0.272727273$$

$$y=\frac{9}{11}\approx 0.818181818$$

Solution Steps

Consider the first equation. Use the distributive property to multiply -5 by 1-3x.

$$2x-5+15x=1-3\left(1-2x\right)$$

Combine 2x and 15x to get 17x.

$$17x-5=1-3\left(1-2x\right)$$

Use the distributive property to multiply -3 by 1-2x.

$$17x-5=1-3+6x$$

Subtract 3 from 1 to get -2.

$$17x-5=-2+6x$$

Subtract 6x from both sides.

$$17x-5-6x=-2$$

Combine 17x and -6x to get 11x.

$$11x-5=-2$$

Add 5 to both sides.

$$11x=-2+5$$

Add -2 and 5 to get 3.

$$11x=3$$

Divide both sides by 11.

$$x=\frac{3}{11}$$

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

$$2\times \frac{3}{11}-5+5y=1-3+6\times \frac{3}{11}$$

Multiply 2 and \frac{3}{11} to get \frac{6}{11}.

$$\frac{6}{11}-5+5y=1-3+6\times \frac{3}{11}$$

Subtract 5 from \frac{6}{11} to get -\frac{49}{11}.

$$-\frac{49}{11}+5y=1-3+6\times \frac{3}{11}$$

Subtract 3 from 1 to get -2.

$$-\frac{49}{11}+5y=-2+6\times \frac{3}{11}$$

Multiply 6 and \frac{3}{11} to get \frac{18}{11}.

$$-\frac{49}{11}+5y=-2+\frac{18}{11}$$

Add -2 and \frac{18}{11} to get -\frac{4}{11}.

$$-\frac{49}{11}+5y=-\frac{4}{11}$$

Add \frac{49}{11} to both sides.

$$5y=-\frac{4}{11}+\frac{49}{11}$$

Add -\frac{4}{11} and \frac{49}{11} to get \frac{45}{11}.

$$5y=\frac{45}{11}$$

Divide both sides by 5.

$$y=\frac{\frac{45}{11}}{5}$$

Express \frac{\frac{45}{11}}{5} as a single fraction.

$$y=\frac{45}{11\times 5}$$

Multiply 11 and 5 to get 55.

$$y=\frac{45}{55}$$

Reduce the fraction \frac{45}{55} to lowest terms by extracting and canceling out 5.

$$y=\frac{9}{11}$$

The system is now solved.

$$x=\frac{3}{11} y=\frac{9}{11}$$