Its a word problem in algebra 1 that i need on step by step ? - norachai and castel each improve their yards by planting rose bushes and geraniums. norachai spent $13 on 1 rose bush and 1 geranium. castel spent $46 on 1 rose bush and 4 geraniums. what is the cost of one rose bush and the cost of one geranium?

Cost of one rose bush =  $2 and cost of 1 geranium = $11

Step-by-step explanation:

lets assume cost of one rose bush = $x

lets assume cost of one geranium = $y

Given that Norachai spent $13 on 1 rose and 1 geranium

⇒ 1 × (cost of one rose bush) + 1× (cost of one geranium) = 13

⇒ 1x + 1y = 13     equation 1

Also given that Castel spent $46 on 1 rose bush and 4 geraniums

⇒1 × (cost of one rose bush) + 4× (cost of one geranium) = 46

⇒ 1x + 4y = 46    equation 2

Now we are having following two equations which will be used to find the value of x and y

1x + 1y = 13     equation 1

1x + 4y = 46    equation 2

lets modify equation 1 to get value of  y in terms of x and name that equation as equation 3

1x + 1y = 13     equation 1

⇒ y = 13 - x    equation 3

On substituting value of y from equation 3 in equation 2 we get

1x + 4 × ( 13 - x ) = 46

⇒ x + 52-4x =46

⇒ -3x = 46-52

⇒     x = (-6)/(-3) = 2

on substituting calculated value of x that is 2 in equation 3 we get

y = 13 -2 = 11

so on solving the equations we get x = 2 and y = 11.

Hence cost of 1 rose bush = $x = $2 and cost of 1 geranium = $y = $11