Solve {l}{7x+109=3}{2x-5y=7}

$$\left\{ \begin{array} { l } { 7 x + 109 = 3 } \\ { 2 x - 5 y = 7 } \end{array} \right.$$

Solve for x, y

$$x = -\frac{106}{7} = -15\frac{1}{7} \approx -15.142857143$$

$$y = -\frac{261}{35} = -7\frac{16}{35} \approx -7.457142857$$

Solution Steps

Consider the first equation. Subtract 109 from both sides.

$$7x=3-109$$

Subtract 109 from 3 to get -106.

$$7x=-106$$

Divide both sides by 7.

$$x=-\frac{106}{7}$$

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

$$2\left(-\frac{106}{7}\right)-5y=7$$

Multiply 2 and -\frac{106}{7} to get -\frac{212}{7}.

$$-\frac{212}{7}-5y=7$$

Add \frac{212}{7} to both sides.

$$-5y=7+\frac{212}{7}$$

Add 7 and \frac{212}{7} to get \frac{261}{7}.

$$-5y=\frac{261}{7}$$

Divide both sides by -5.

$$y=\frac{\frac{261}{7}}{-5}$$

Express \frac{\frac{261}{7}}{-5} as a single fraction.

$$y=\frac{261}{7\left(-5\right)}$$

Multiply 7 and -5 to get -35.

$$y=\frac{261}{-35}$$

Fraction \frac{261}{-35} can be rewritten as -\frac{261}{35} by extracting the negative sign.

$$y=-\frac{261}{35}$$

The system is now solved.

$$x=-\frac{106}{7} y=-\frac{261}{35}$$