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

Answer:

• (4 1/3, 1/9)

Step-by-step 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

Answer 2

Answer:

see below

Step-by-step 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

$x = 4 \frac{1}{3} \\ y = \frac{1}{9}$

let's justify the (I) equation

$4(4 \frac{1}{3}) + 6( \frac{1}{9} ) = 18$

$4( \frac{13}{3} ) +6 (\frac{1}{9}) = 18$

$\frac{52}{3} + \frac{2}{3} = 18$

$\frac{52 + 2}{3} = 18$

$\frac{54}{3} = 18$

$18 = 18$

proven

let's justify the ii equation:

$\frac{1}{9} + 2 = \frac{1}{3} ( \frac{13}{3} + 2)$

$\frac{19}{9} = \frac{1}{3} \times \frac{19}{3}$

$\frac{19}{9} = \frac{19}{9}$

proven