Question

1. Which of the ordered pairs in the form (x, y) is a solution of this equation?

3x + 2y = 6

A. (4, −3)
B. (8, −5)
C. None are solutions.
D. (−2, 0)

2. Solve the equation for y.
2x+5y=5

A. y=-10x+25
B. y=-2/5 x+1
C. y=2/5 x+5
D. y=2/5 x+1

3. Which statement is true about the equation?
3y – 6x = –3

A. When x = −4, y = 7 and when x = 2, y = 3.
B. When x = −4, y = −7 and when x = 2, y = −3.
C. When x = −4, y = 9 and when x = 2, y = 3.
D. When x = −4, y = −9 and when x = 2, y = 3.

Answer 1

Part 1: Option A :
`(4,-3)` is the solution to the equation
`3 x+2 y=6`

Part 2: Option B :
`y=-(2)/(5) x+1` is the equation for y.

Part 3: Option D: When
`x=-4, y=-9` and when
`x=2, y=3`

Step-by-step explanation:

Part 1: The equation is
`3 x+2 y=6`

The solution of the equation can be determined when the ordered pair satisfies the equation
`3 x+2 y=6`

Substituting
`(4,-3)` in the equation
`3 x+2 y=6`, we have,

`3(4)+2(-3)=6`

`12-6=6`

`6=6`

Thus, the ordered pair
`(4,-3)` satisfies the equation
`3 x+2 y=6`

Hence, Option A is the correct answer.

Part 2: The equation is
`2 x+5 y=5`

Let us solve the equation for y.

`5y=-2x+5`

Dividing both sides by 5, we have,

`y=-(2)/(5) x+1`

Thus, the equation for y is
`y=-(2)/(5) x+1`

Hence, Option B is the correct answer.

Part 3: The equation is
`3 y-6 x=-3`

To determine the true statement, we need to substitute the value of x and y in the equation and find out which x and y values results in the equation to be true.

When
`x=-4, y=-9` and when
`x=2, y=3`

First, let us substitute
`x=-4, y=-9` in the equation
`3 y-6 x=-3`

`3(-9)-6(-4)=-3`

`-27+24=-3`

`-3=-3`

Now, let us substitute
`x=2, y=3` in the equation
`3 y-6 x=-3`

`3(3)-6(2)=-3`

`9-12=-3`

`-3=-3`

Thus, the equation is true when
`x=-4, y=-9` and when
`x=2, y=3`

Hence, Option D is the correct answer.