Solve {l}{4x+5=2}{x-y=1}

$$\left. \begin{array} { l } { 4 x + 5 = 2 } \\ { x - y = 1 } \end{array} \right.$$

Solve for x, y

$$x=-\frac{3}{4}=-0.75$$

$$y = -\frac{7}{4} = -1\frac{3}{4} = -1.75$$

Solution Steps

Consider the first equation. Subtract 5 from both sides.

$$4x=2-5$$

Subtract 5 from 2 to get -3.

$$4x=-3$$

Divide both sides by 4.

$$x=-\frac{3}{4}$$

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

$$-\frac{3}{4}-y=1$$

Add \frac{3}{4} to both sides.

$$-y=1+\frac{3}{4}$$

Add 1 and \frac{3}{4} to get \frac{7}{4}.

$$-y=\frac{7}{4}$$

Divide both sides by -1.

$$y=\frac{\frac{7}{4}}{-1}$$

Express \frac{\frac{7}{4}}{-1} as a single fraction.

$$y=\frac{7}{4\left(-1\right)}$$

Multiply 4 and -1 to get -4.

$$y=\frac{7}{-4}$$

Fraction \frac{7}{-4} can be rewritten as -\frac{7}{4} by extracting the negative sign.

$$y=-\frac{7}{4}$$

The system is now solved.

$$x=-\frac{3}{4} y=-\frac{7}{4}$$