Solve {l}{x=2y-3}{4x-7=x}

$$\left. \begin{array} { l } { x = 2 y - 3 } \\ { 4 x - 7 = x } \end{array} \right.$$

Solve for x, y

$$x = \frac{7}{3} = 2\frac{1}{3} \approx 2.333333333$$

$$y = \frac{8}{3} = 2\frac{2}{3} \approx 2.666666667$$

Solution Steps

Consider the second equation. Subtract x from both sides.

$$4x-7-x=0$$

Combine 4x and -x to get 3x.

$$3x-7=0$$

Add 7 to both sides. Anything plus zero gives itself.

$$3x=7$$

Divide both sides by 3.

$$x=\frac{7}{3}$$

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

$$\frac{7}{3}=2y-3$$

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

$$2y-3=\frac{7}{3}$$

Add 3 to both sides.

$$2y=\frac{7}{3}+3$$

Add \frac{7}{3} and 3 to get \frac{16}{3}.

$$2y=\frac{16}{3}$$

Divide both sides by 2.

$$y=\frac{\frac{16}{3}}{2}$$

Express \frac{\frac{16}{3}}{2} as a single fraction.

$$y=\frac{16}{3\times 2}$$

Multiply 3 and 2 to get 6.

$$y=\frac{16}{6}$$

Reduce the fraction \frac{16}{6} to lowest terms by extracting and canceling out 2.

$$y=\frac{8}{3}$$

The system is now solved.

$$x=\frac{7}{3} y=\frac{8}{3}$$