Question

Solve system with substitution

Answer 1

Answer:

The cost of 1 Rose Bush= $ 8

The cost of 1 Shrub =  $12.

Step-by-step explanation:

The cost of 11 rose bushes and 4 shrubs =  $136

The cost of 2 rose bushes and 11 shrubs =  $148

Let the cost of one rose bush =  $x

and the cost of one shrub  =  $ y

Now, according to the question:

11 x + 4 y = 136

and 2 x + 11 y  = 148

From (1), we get that 11x  = 136 - 4y

or, $x = \frac{136 - 4y}{11}$

Substitute this value of x in equation (2), we get

$2 x + 11 y = 148 \implies 2( \frac{136 - 4y}{11}) + 11y = 148$

or, $( \frac{272 - 8y}{11}) + 11y = 148 \implies 272 - 8y + 121y = 1628$

or, 113 y = 1356

or, y = 1356/113 = 12

⇒ y = 12, So $x = \frac{136 - 4y}{11} = \frac{136 -12(4)}{11} = \frac{136 - 48}{11} = 8$

or, x  =8 and  y = 12 is the solution of the above system.

Hence, the cost of 1 rose bush  = $x = $8

and  The cost of 1 shrub = $ y = $12.