Solve {l}{-12+2y+4=-21+y+11}{-9-13y-2=-6-ay+1}

$$\left\{ \begin{array} { l } { - 12 + 2 y + 4 = - 21 + y + 11 } \\ { - 9 - 13 y - 2 = - 6 - a y + 1 } \end{array} \right.$$

Solve for y, a

$$y=-2$$

$$a=10$$

Solution Steps

Consider the first equation. Add -12 and 4 to get -8.

$$-8+2y=-21+y+11$$

Add -21 and 11 to get -10.

$$-8+2y=-10+y$$

Subtract y from both sides.

$$-8+2y-y=-10$$

Combine 2y and -y to get y.

$$-8+y=-10$$

Add 8 to both sides.

$$y=-10+8$$

Add -10 and 8 to get -2.

$$y=-2$$

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

$$-9-13\left(-2\right)-2=-6-a\left(-2\right)+1$$

Multiply -13 and -2 to get 26.

$$-9+26-2=-6-a\left(-2\right)+1$$

Add -9 and 26 to get 17.

$$17-2=-6-a\left(-2\right)+1$$

Subtract 2 from 17 to get 15.

$$15=-6-a\left(-2\right)+1$$

Multiply -1 and -2 to get 2.

$$15=-6+2a+1$$

Add -6 and 1 to get -5.

$$15=-5+2a$$

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

$$-5+2a=15$$

Add 5 to both sides.

$$2a=15+5$$

Add 15 and 5 to get 20.

$$2a=20$$

Divide both sides by 2.

$$a=\frac{20}{2}$$

Divide 20 by 2 to get 10.

$$a=10$$

The system is now solved.

$$y=-2 a=10$$