Question

Help me please with math

Answer 1

To check if an ordered pair (
`a`,
`b`) is a solution of a system of equation, we just need to replace
`x` with
`a` and
`y` with
`b` in the system of equations and check if satisfies both equations:

a) Ordered pair: (2,3)

`\left \{ {{4x-y=3} \atop {-16x+4y=-12}} \right.`

`\left \{ {{4(2)-3=3} \atop {-16(2)+4(3)=-12}} \right.`

`\left \{ {{8-3=3} \atop {-32+12=-12}} \right.`

`\left \{ {{5=3} \atop {-20=-12}} \right.`

We can conclude that the ordered pair (2,3) is not the solution of the system of equations because it doesn't satisfy at least one equation. Therefore, the correct choice is D.

b) Ordered pair (0,-3)

`\left \{ {{4x-y=3} \atop {-16x+4y=-12}} \right.`

`\left \{ {{4(0)-(-3)=3} \atop {-16(0)+4(-3)=-12}} \right.`

`\left \{ {{3=3} \atop {-12)=-12}} \right.`

We can conclude that the ordered pair (0,3) is a solution of the system of equations because it satisfies both equations. Therefore, the correct choice is B.

c) Ordered pair (3,9)

`\left \{ {{4x-y=3} \atop {-16x+4y=-12}} \right.`

`\left \{ {{4(3)-9=3} \atop {-16(3)+4(9)=-12}} \right.`

`\left \{ {{12-9=3} \atop {-48+36=-12}} \right.`

`\left \{ {{3=3} \atop {-12=-12}} \right.`

We can conclude that the ordered pair (3,9) is a solution of the system of equations because it satisfies both equations. Therefore, the correct choice is A.

Answer 2

the equation is the same line or equation 1 = equation 2

a. D) No, satisfies none
b. A or B
c. A or D