Solve {l}{(2a-1)=8-x}{3y=x-12}

$$\left\{ \begin{array} { l } { ( 2 a - 1 ) = 8 - x } \\ { 3 y = x - 12 } \end{array} \right.$$

Solve for x, y

$$x=9-2a$$

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

Steps Using Substitution

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

$$8-x=2a-1$$

Subtract 8 from both sides.

$$-x=2a-1-8$$

Subtract 8 from -1 to get -9.

$$-x=2a-9$$

Consider the second equation. Subtract x from both sides.

$$3y-x=-12$$

To solve a pair of equations using substitution, first solve one of the equations for one of the variables. Then substitute the result for that variable in the other equation.

$$-x=2a-9,-x+3y=-12$$

Pick one of the two equations which is more simple to solve for x by isolating x on the left hand side of the equal sign.

$$-x=2a-9$$

Divide both sides by -1.

$$x=9-2a$$

Substitute -2a+9 for x in the other equation, -x+3y=-12.

$$-\left(9-2a\right)+3y=-12$$

Subtract 2a-9 from both sides of the equation.

$$3y=-2a-3$$

Divide both sides by 3.

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

The system is now solved.

$$x=9-2a,y=-\frac{2a}{3}-1$$