Solve {l}{202.65x=2*8.314y}{10*4.65=2*8.314y}

$$\left\{ \begin{array} { l } { 202.65 x = 2 \times 8.314 y } \\ { 10 \times 4.65 = 2 \times 8.314 y } \end{array} \right.$$

Solve for x, y

$$x=\frac{310}{1351}\approx 0.22945966$$

$$y = \frac{11625}{4157} = 2\frac{3311}{4157} \approx 2.796487852$$

Steps Using Substitution

Consider the second equation. Swap sides so that all variable terms are on the left hand side.

$$2\times 8.314y=10\times 4.65$$

Consider the first equation. Subtract 2\times 8.314y from both sides.

$$202.65x-2\times 8.314y=0$$

Reorder the terms.

$$-y\left(2\times 8.314\right)+202.65x=0$$

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.

$$2\times 8.314y=10\times 4.65,\left(-2\times 8.314\right)y+202.65x=0$$

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.

$$2\times 8.314y=10\times 4.65$$

Divide both sides of the equation by 16.628, which is the same as multiplying both sides by the reciprocal of the fraction.

$$y=\frac{11625}{4157}$$

Substitute \frac{11625}{4157} for y in the other equation, \left(-2\times 8.314\right)y+202.65x=0.

$$\left(-2\times 8.314\right)\times \frac{11625}{4157}+202.65x=0$$

Multiply -2\times 8.314 times \frac{11625}{4157}.

$$-46.5+202.65x=0$$

Add 46.5 to both sides of the equation.

$$202.65x=46.5$$

Divide both sides of the equation by 202.65, which is the same as multiplying both sides by the reciprocal of the fraction.

$$x=\frac{310}{1351}$$

The system is now solved.

$$y=\frac{11625}{4157},x=\frac{310}{1351}$$