Solve {l}{4x-2y-7x=-1}{12x+12y-7x-12y=15}

$$\left\{ \begin{array} { l } { 4 x - 2 y - 7 x = - 1 } \\ { 12 x + 12 y - 7 x - 12 y = 15 } \end{array} \right.$$

Solve for x, y

$$x=3$$

$$y=-4$$

Solution Steps

Consider the first equation. Combine 4x and -7x to get -3x.

$$-3x-2y=-1$$

Consider the second equation. Combine 12x and -7x to get 5x.

$$5x+12y-12y=15$$

Combine 12y and -12y to get 0.

$$5x=15$$

Divide both sides by 5.

$$x=\frac{15}{5}$$

Divide 15 by 5 to get 3.

$$x=3$$

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

$$-3\times 3-2y=-1$$

Multiply -3 and 3 to get -9.

$$-9-2y=-1$$

Add 9 to both sides.

$$-2y=-1+9$$

Add -1 and 9 to get 8.

$$-2y=8$$

Divide both sides by -2.

$$y=\frac{8}{-2}$$

Divide 8 by -2 to get -4.

$$y=-4$$

The system is now solved.

$$x=3 y=-4$$