Question

Graph the system of equations on graph paper. {8x+6y=48 {2x−3y=−6 Which statements are true about the solution to the system of equations? Select each correct answer.

The x-coordinate of the solution is −3 .

The x-coordinate of the solution is 3.

The ordered pair that is the solution to the system lies in Quadrant I .

The y-coordinate of the solution is 4.

The ordered pair that is the solution to the system lies in Quadrant II .

The y-coordinate of the solution is 3.

Answer 1

The x-coordinate of the solution is 3.

The ordered pair that is the solution to the system lies in Quadrant I

The y-coordinate of the solution is 4

The graph in the attached figure

Explanation:

we have

`8x+6y=48` ----> equation A

`2x-3y=-6` ----> equation B

To graph the system of equations , find the intercepts of each line

Line A

Find the y-intercept (value of y when the value of x is equal to zero)

For x=0

`8(0)+6y=48\\y=8`

The y-intercept is the point is (0,8)

Find the x-intercept (value of x when the value of y is equal to zero)

For y=0

`8x+6(0)=48\\x=6`

The x-intercept is the point is (6,0)

Plot the points (0,8) and (6,0), and connect them to graph the line A

Line B

Find the y-intercept (value of y when the value of x is equal to zero)

For x=0

`2(0)-3y=-6\\y=2`

The y-intercept is the point is (0,2)

Find the x-intercept (value of x when the value of y is equal to zero)

For y=0

`2x-3(0)=-6\\x=-3`

The x-intercept is the point is (-3,0)

Plot the points (0,2) and (-3,0), and connect them to graph the line B

Remember that the solution of the system of equations is the intersection point both graphs

The solution of the system is the point (3,4)

The graph in the attached figure

Verify each statement

case 1) The x-coordinate of the solution is −3

The statement is false

Because the x-coordinate of the solution is 3

case 2) The x-coordinate of the solution is 3.

The statement is true (see the explanation)

case 3) The ordered pair that is the solution to the system lies in Quadrant I

The statement is true

Because, the x-coordinate and the y-coordinate of the solution are positive values

case 4) The y-coordinate of the solution is 4

The statement is true (see the explanation)

case 5) The ordered pair that is the solution to the system lies in Quadrant II

The statement is false

Because, the ordered pair that is the solution to the system lies in Quadrant I

case 6) The y-coordinate of the solution is 3

The statement is false

Because, the y-coordinate of the solution is 4