Solve {l}{x=4y+6}{y=4y+b/3}

$$\left\{ \begin{array} { l } { x = 4 y + 6 } \\ { y = \frac { 4 y + b } { 3 } } \end{array} \right.$$

Solve for x, y

$$x=6-4b$$

$$y=-b$$

Steps Using Substitution

Consider the second equation. Divide each term of 4y+b by 3 to get \frac{4}{3}y+\frac{1}{3}b.

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

Subtract \frac{4}{3}y from both sides.

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

Combine y and -\frac{4}{3}y to get -\frac{1}{3}y.

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

Consider the first equation. Subtract 4y from both sides.

$$x-4y=6$$

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.

$$-\frac{1}{3}y=\frac{b}{3},-4y+x=6$$

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

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

Multiply both sides by -3.

$$y=-b$$

Substitute -b for y in the other equation, -4y+x=6.

$$-4\left(-b\right)+x=6$$

Multiply -4 times -b.

$$4b+x=6$$

Subtract 4b from both sides of the equation.

$$x=6-4b$$

The system is now solved.

$$y=-b,x=6-4b$$