Question

solve the systems of equations via graphing then check the solution in each equation: 4x+6y=18, (y+2)=1/3(x+2)

Answer 1

see below

Explanation:

to understand this

you need to know about:

• linear equation
• graphing linear equation
• PEMDAS

given equation:

4x+6y=18......(I)

(y+2)=1/3(x+2).......(ii)

let's solve using graph:

the picture is attached

got from the picture

`x = 4 (1)/(3) \\ y = (1)/(9)`

let's justify the (I) equation

`4(4 (1)/(3)) + 6( (1)/(9) ) = 18`

`4( (13)/(3) ) +6 ((1)/(9)) = 18`

`(52)/(3) + (2)/(3) = 18`

`(52 + 2)/(3) = 18`

`(54)/(3) = 18`

`18 = 18`

proven

let's justify the ii equation:

`(1)/(9) + 2 = (1)/(3) ( (13)/(3) + 2)`

`(19)/(9) = (1)/(3) * (19)/(3)`

`(19)/(9) = (19)/(9)`

proven

Answer 2

• (4 1/3, 1/9)

Explanation:

Given system

• 4x + 6y = 18
• (y + 2) = 1/3(x + 2)

Solution is the intersection point:

• (4 1/3, 1/9)

Simplify the first equation:

• 2x + 3y = 9
• 3y = -2x + 9
• y = -2/3x + 3

Check:

• 1/9 = -2/3*4 1/3 + 9
• 1/9 = -26/9 + 9
• 1/9 = (27 - 26)/9
• 1/9 = 1/9

Simplify the second equation:

• y + 2 = 1/3x + 2/3
• y = 1/3x + 2/3 - 2
• y = 1/3x - 4/3

Check:

• 1/9 = 1/3*13/3 - 4/3
• 1/9 = (13 - 12)/9
• 1/9 = 1/9