Solve {l}{4x+5=10}{2x+3y=2}

$$\left. \begin{array} { l } { 4 x + 5 = 10 } \\ { 2 x + 3 y = 2 } \end{array} \right.$$

Solve for x, y

$$x = \frac{5}{4} = 1\frac{1}{4} = 1.25$$

$$y=-\frac{1}{6}\approx -0.166666667$$

Solution Steps

Consider the first equation. Subtract 5 from both sides.

$$4x=10-5$$

Subtract 5 from 10 to get 5.

$$4x=5$$

Divide both sides by 4.

$$x=\frac{5}{4}$$

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

$$2\times \frac{5}{4}+3y=2$$

Multiply 2 and \frac{5}{4} to get \frac{5}{2}.

$$\frac{5}{2}+3y=2$$

Subtract \frac{5}{2} from both sides.

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

Subtract \frac{5}{2} from 2 to get -\frac{1}{2}.

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

Divide both sides by 3.

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

Express \frac{-\frac{1}{2}}{3} as a single fraction.

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

Multiply 2 and 3 to get 6.

$$y=\frac{-1}{6}$$

Fraction \frac{-1}{6} can be rewritten as -\frac{1}{6} by extracting the negative sign.

$$y=-\frac{1}{6}$$

The system is now solved.

$$x=\frac{5}{4} y=-\frac{1}{6}$$