Solve {l}{x-xsqrt{2}=0}{5x+ysqrt{8}=9}

$$\left. \begin{array} { l } { x - x \sqrt { 2 } = 0 } \\ { 5 x + y \sqrt { 8 } = 9 } \end{array} \right.$$

Solve for x, y

$$x=0$$

$$y = \frac{9 \sqrt{2}}{4} \approx 3.181980515$$

Steps Using Substitution

Consider the first equation. Reorder the terms.

$$-\sqrt{2}x+x=0$$

Combine all terms containing x,y.

$$\left(-\sqrt{2}+1\right)x=0$$

Consider the second equation. Factor 8=2^{2}\times 2. Rewrite the square root of the product \sqrt{2^{2}\times 2} as the product of square roots \sqrt{2^{2}}\sqrt{2}. Take the square root of 2^{2}.

$$5x+y\times 2\sqrt{2}=9$$

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.

$$\left(1-\sqrt{2}\right)x=0,5x+2\sqrt{2}y=9$$

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

$$\left(1-\sqrt{2}\right)x=0$$

Divide both sides by -\sqrt{2}+1.

$$x=0$$

Substitute 0 for x in the other equation, 5x+2\sqrt{2}y=9.

$$2\sqrt{2}y=9$$

Divide both sides by 2\sqrt{2}.

$$y=\frac{9\sqrt{2}}{4}$$

The system is now solved.

$$x=0,y=\frac{9\sqrt{2}}{4}$$