Solve {l}{1x+2y=-14}{7(-2y-21)+2y=-19}

$$\left. \begin{array} { l } { 1 x + 2 y = - 14 } \\ { 7 ( - 2 y - 21 ) + 2 y = - 19 } \end{array} \right.$$

Solve for x, y

$$x = \frac{22}{3} = 7\frac{1}{3} \approx 7.333333333$$

$$y = -\frac{32}{3} = -10\frac{2}{3} \approx -10.666666667$$

Solution Steps

Consider the second equation. Use the distributive property to multiply 7 by -2y-21.

$$-14y-147+2y=-19$$

Combine -14y and 2y to get -12y.

$$-12y-147=-19$$

Add 147 to both sides.

$$-12y=-19+147$$

Add -19 and 147 to get 128.

$$-12y=128$$

Divide both sides by -12.

$$y=\frac{128}{-12}$$

Reduce the fraction \frac{128}{-12} to lowest terms by extracting and canceling out 4.

$$y=-\frac{32}{3}$$

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

$$1x+2\left(-\frac{32}{3}\right)=-14$$

Multiply 2 and -\frac{32}{3} to get -\frac{64}{3}.

$$1x-\frac{64}{3}=-14$$

Add \frac{64}{3} to both sides.

$$1x=-14+\frac{64}{3}$$

Add -14 and \frac{64}{3} to get \frac{22}{3}.

$$1x=\frac{22}{3}$$

Divide both sides by 1.

$$x=\frac{\frac{22}{3}}{1}$$

Express \frac{\frac{22}{3}}{1} as a single fraction.

$$x=\frac{22}{3\times 1}$$

Multiply 3 and 1 to get 3.

$$x=\frac{22}{3}$$

The system is now solved.

$$x=\frac{22}{3} y=-\frac{32}{3}$$