[tex]12)\\\left\{\begin{array}{ccc}y=-2x+3&(*)\\2x+5y=7\end{array}\right\qquad\text{put}\ (*)\ \text{to the second equation}\\\\2x+5(-2x+3)=7\qquad\text{use distributive property}\\2x+(5)(-2x)+(5)(3)=7\\2x-10x+15=7\qquad\text{subtract 15 from both sides}\\-8x=-8\qquad\text{divide both sides by (-8)}\\\boxed{x=1}\\\\\text{Put the value of x to}\ (*)\\\\y=-2(1)+3\\y=-2+3\\\boxed{y=1}\\\\Answer:\ x=1,\ y=1\to(1,\ 1)[/tex]
[tex]14)\\\left\{\begin{array}{ccc}x=y-4&(*)\\x-2y=-6\end{array}\right\qquad\text{put}\ (*)\ \text{tu the second equation}\\\\(y-4)-2y=-6\\y-4-2y=-6\qquad\text{add 4 to both sides}\\-y=-2\qquad\text{change the signs}\\\boxed{y=2}\\\\\text{Put the value of y to}\ (*)\\\\x=2-4\\\boxed{x=-2}\\\\Answer:\ x=-2,\ y=2\to(-2,\ 2)[/tex]
[tex]16)\\\left\{\begin{array}{ccc}x=-4y+3&(*)\\5x-3y=-31\end{array}\right\qquad\text{put}\ (*)\ \text{to the second equation}\\\\5(-4y+3)-3y=-31\qquad\text{use distributive property}\\(5)(-4y)+(5)(3)-3y=-31\\-20y+15-3y=-31\qquad\text{subtract 15 from both sides}\\-23y=-46\qquad\text{divide both sides by (-23)}\\\boxed{y=2}\\\\\text{Put the value of y to }\ (*)\\\\x=-4(2)+3\\x=-8+3\\\boxed{x=-5}\\\\Answer:\ x=-5,\ y=2\to(-5,\ 2)[/tex]
