Solve {l}{x+3=5y}{2x+y=y+1}

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

Solve for x, y

$$x=\frac{1}{2}=0.5$$

$$y=\frac{7}{10}=0.7$$

Solution Steps

Consider the first equation. Subtract 5y from both sides.

$$x+3-5y=0$$

Subtract 3 from both sides. Anything subtracted from zero gives its negation.

$$x-5y=-3$$

Consider the second equation. Subtract y from both sides.

$$2x+y-y=1$$

Combine y and -y to get 0.

$$2x=1$$

Divide both sides by 2.

$$x=\frac{1}{2}$$

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

$$\frac{1}{2}-5y=-3$$

Subtract \frac{1}{2} from both sides.

$$-5y=-3-\frac{1}{2}$$

Subtract \frac{1}{2} from -3 to get -\frac{7}{2}.

$$-5y=-\frac{7}{2}$$

Divide both sides by -5.

$$y=\frac{-\frac{7}{2}}{-5}$$

Express \frac{-\frac{7}{2}}{-5} as a single fraction.

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

Multiply 2 and -5 to get -10.

$$y=\frac{-7}{-10}$$

Fraction \frac{-7}{-10} can be simplified to \frac{7}{10} by removing the negative sign from both the numerator and the denominator.

$$y=\frac{7}{10}$$

The system is now solved.

$$x=\frac{1}{2} y=\frac{7}{10}$$