Solve {l}{(x+3)*(x-1)-(x+2)*(x-3)=15}{(6z+5)*(z-3)-(2z-1)*(3z+2)=1}

$$\left. \begin{array} { l } { ( x + 3 ) \cdot ( x - 1 ) - ( x + 2 ) \cdot ( x - 3 ) = 15 } \\ { ( 6 z + 5 ) \cdot ( z - 3 ) - ( 2 z - 1 ) \cdot ( 3 z + 2 ) = 1 } \end{array} \right.$$

Solve for x, z

$$x=4$$

$$z=-1$$

Solution Steps

Consider the first equation. Use the distributive property to multiply x+3 by x-1 and combine like terms.

$$x^{2}+2x-3-\left(x+2\right)\left(x-3\right)=15$$

Use the distributive property to multiply x+2 by x-3 and combine like terms.

$$x^{2}+2x-3-\left(x^{2}-x-6\right)=15$$

To find the opposite of x^{2}-x-6, find the opposite of each term.

$$x^{2}+2x-3-x^{2}+x+6=15$$

Combine x^{2} and -x^{2} to get 0.

$$2x-3+x+6=15$$

Combine 2x and x to get 3x.

$$3x-3+6=15$$

Add -3 and 6 to get 3.

$$3x+3=15$$

Subtract 3 from both sides.

$$3x=15-3$$

Subtract 3 from 15 to get 12.

$$3x=12$$

Divide both sides by 3.

$$x=\frac{12}{3}$$

Divide 12 by 3 to get 4.

$$x=4$$

Consider the second equation. Use the distributive property to multiply 6z+5 by z-3 and combine like terms.

$$6z^{2}-13z-15-\left(2z-1\right)\left(3z+2\right)=1$$

Use the distributive property to multiply 2z-1 by 3z+2 and combine like terms.

$$6z^{2}-13z-15-\left(6z^{2}+z-2\right)=1$$

To find the opposite of 6z^{2}+z-2, find the opposite of each term.

$$6z^{2}-13z-15-6z^{2}-z+2=1$$

Combine 6z^{2} and -6z^{2} to get 0.

$$-13z-15-z+2=1$$

Combine -13z and -z to get -14z.

$$-14z-15+2=1$$

Add -15 and 2 to get -13.

$$-14z-13=1$$

Add 13 to both sides.

$$-14z=1+13$$

Add 1 and 13 to get 14.

$$-14z=14$$

Divide both sides by -14.

$$z=\frac{14}{-14}$$

Divide 14 by -14 to get -1.

$$z=-1$$

The system is now solved.

$$x=4 z=-1$$