Solve {l}{y=frac{sqrt{15}}{14}}{sqrt{15}x+y-4sqrt{15}=1}

$$\left\{ \begin{array} { l } { y = \frac { \sqrt { 15 } } { 14 } } \\ { \sqrt { 15 } x + y - 4 \sqrt { 15 } = 1 } \end{array} \right.$$

Solve for y, x

$$x=\frac{\sqrt{15}}{15}+\frac{55}{14}\approx 4.186770318$$

$$y=\frac{\sqrt{15}}{14}\approx 0.276641668$$

Steps Using Substitution

To solve a pair of equations using substitution, first solve one of the equations for one of the variables. Then substitute the result for that variable in the other equation.

$$y=\frac{\sqrt{15}}{14},y+\sqrt{15}x-4\sqrt{15}=1$$

Pick one of the two equations which is more simple to solve for y by isolating y on the left hand side of the equal sign.

$$y=\frac{\sqrt{15}}{14}$$

Substitute \frac{\sqrt{15}}{14} for y in the other equation, y+\sqrt{15}x-4\sqrt{15}=1.

$$\frac{\sqrt{15}}{14}+\sqrt{15}x-4\sqrt{15}=1$$

Add \frac{\sqrt{15}}{14} to -4\sqrt{15}.

$$\sqrt{15}x-\frac{55\sqrt{15}}{14}=1$$

Add \frac{55\sqrt{15}}{14} to both sides of the equation.

$$\sqrt{15}x=\frac{55\sqrt{15}}{14}+1$$

Divide both sides by \sqrt{15}.

$$x=\frac{\sqrt{15}}{15}+\frac{55}{14}$$

The system is now solved.

$$y=\frac{\sqrt{15}}{14},x=\frac{\sqrt{15}}{15}+\frac{55}{14}$$