Solve {l}{y+1/4=1+2/3}{2x-3y=1}

$$\left\{ \begin{array} { l } { \frac { y + 1 } { 4 } = \frac { 1 + 2 } { 3 } } \\ { 2 x - 3 y = 1 } \end{array} \right.$$

Solve for y, x

$$x=5$$

$$y=3$$

Solution Steps

Consider the first equation. Multiply both sides of the equation by 12, the least common multiple of 4,3.

$$3\left(y+1\right)=4\left(1+2\right)$$

Use the distributive property to multiply 3 by y+1.

$$3y+3=4\left(1+2\right)$$

Add 1 and 2 to get 3.

$$3y+3=4\times 3$$

Multiply 4 and 3 to get 12.

$$3y+3=12$$

Subtract 3 from both sides.

$$3y=12-3$$

Subtract 3 from 12 to get 9.

$$3y=9$$

Divide both sides by 3.

$$y=\frac{9}{3}$$

Divide 9 by 3 to get 3.

$$y=3$$

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

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

Multiply -3 and 3 to get -9.

$$2x-9=1$$

Add 9 to both sides.

$$2x=1+9$$

Add 1 and 9 to get 10.

$$2x=10$$

Divide both sides by 2.

$$x=\frac{10}{2}$$

Divide 10 by 2 to get 5.

$$x=5$$

The system is now solved.

$$y=3 x=5$$