Solve {l}{y=-2x+2}{4y+3=-12}

$$\left\{ \begin{array} { l } { y = - 2 x + 2 } \\ { 4 y + 3 = - 12 } \end{array} \right.$$

Solve for y, x

$$x = \frac{23}{8} = 2\frac{7}{8} = 2.875$$

$$y = -\frac{15}{4} = -3\frac{3}{4} = -3.75$$

Solution Steps

Consider the second equation. Subtract 3 from both sides.

$$4y=-12-3$$

Subtract 3 from -12 to get -15.

$$4y=-15$$

Divide both sides by 4.

$$y=-\frac{15}{4}$$

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

$$-\frac{15}{4}=-2x+2$$

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

$$-2x+2=-\frac{15}{4}$$

Subtract 2 from both sides.

$$-2x=-\frac{15}{4}-2$$

Subtract 2 from -\frac{15}{4} to get -\frac{23}{4}.

$$-2x=-\frac{23}{4}$$

Divide both sides by -2.

$$x=\frac{-\frac{23}{4}}{-2}$$

Express \frac{-\frac{23}{4}}{-2} as a single fraction.

$$x=\frac{-23}{4\left(-2\right)}$$

Multiply 4 and -2 to get -8.

$$x=\frac{-23}{-8}$$

Fraction \frac{-23}{-8} can be simplified to \frac{23}{8} by removing the negative sign from both the numerator and the denominator.

$$x=\frac{23}{8}$$

The system is now solved.

$$y=-\frac{15}{4} x=\frac{23}{8}$$