Question

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

A. (1, 3)

B. (3, 4)

C. (2, 3)

D. (3, 2)

The first picture on the bottom this for question 1.



2.) The system of equations is graphed on the coordinate plane.

y = − x − 2
y = 3 x + 2

Enter the coordinates of the solution to the system of equations in the boxes.

( __ , __ )

The second picture on the bottom is for question 2.

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

$(-1,-1)$