Question

1.) What is the best approximation of the solution to the system to the nearest integer values?

Answer 1

For number one, the answer is C. (2,3).

For number two, the answer is (-1, -1). 

((Simply find the intersection between the two lines to get your solution. 

Answer 2

Part 1) we have

$5x+2y=16$ ------> equation A

$x+3y=12$

$x=12-3y$ ------> equation B

Substitute the equation B in equation A

$5[12-3y]+2y=16$

$60-15y+2y=16$

$13y=44$

$y=44/13=3.38$

Find the value of x

$x=12-3(44/13)=1.85$

the best approximation is the point $(2.3)$

therefore

the answer Part 1) is the option C

$(2.3)$

Part 2) we have

$y=-x-2$ ------> equation A

$y=3x+2$ ------> equation B

equate equation A and equation B

$-x-2=3x+2$

$4x=-4$

$x=-1$

Find the value of y

$y=-(-1)-2=-1$

the solution is the point $(-1,-1)$

therefore

the answer Part 2) is

$(-1,-1)$