Solve {l}{-2x/7=9/14}{2a-(1+5a)=4a}

$$\left. \begin{array} { l } { \frac { - 2 x } { 7 } = \frac { 9 } { 14 } } \\ { 2 a - ( 1 + 5 a ) = 4 a } \end{array} \right.$$

Solve for x, a

$$x = -\frac{9}{4} = -2\frac{1}{4} = -2.25$$

$$a=-\frac{1}{7}\approx -0.142857143$$

Solution Steps

Consider the first equation. Multiply both sides by 7.

$$-2x=\frac{9}{14}\times 7$$

Multiply \frac{9}{14} and 7 to get \frac{9}{2}.

$$-2x=\frac{9}{2}$$

Divide both sides by -2.

$$x=\frac{\frac{9}{2}}{-2}$$

Express \frac{\frac{9}{2}}{-2} as a single fraction.

$$x=\frac{9}{2\left(-2\right)}$$

Multiply 2 and -2 to get -4.

$$x=\frac{9}{-4}$$

Fraction \frac{9}{-4} can be rewritten as -\frac{9}{4} by extracting the negative sign.

$$x=-\frac{9}{4}$$

Consider the second equation. To find the opposite of 1+5a, find the opposite of each term.

$$2a-1-5a=4a$$

Combine 2a and -5a to get -3a.

$$-3a-1=4a$$

Subtract 4a from both sides.

$$-3a-1-4a=0$$

Combine -3a and -4a to get -7a.

$$-7a-1=0$$

Add 1 to both sides. Anything plus zero gives itself.

$$-7a=1$$

Divide both sides by -7.

$$a=-\frac{1}{7}$$

The system is now solved.

$$x=-\frac{9}{4} a=-\frac{1}{7}$$