Simultaneous equations?

Question

Roses £x each . Shrubs £y each

(1) Megan buys 4 roses and 3 shrubs
She pays £33

Use this information to write down an equation in x and y ....

(2) Josh buys 6 roses and 6 shrubs
He pays £57

Use this information to write down another equation in x and y...

(3) Solve your equations simultaneously to find the values of x and y. Do not use trial and improvement

my answer for (1) was 4x + 3y = £33 but I do not know if this is right. and I have no clue how to do (3) thanks for your help

Answer 1

(1) The equation is 4x+3y=33. This is because the cost of four roses and 3 shrubs totals to $33. So your answer to 1 is correct.

(2) The equation is 6x+6y=57.

(3) In order to solve these two equations, you must use systems of equations. There are two methods; elimination and substitution. In this scenario, elimination is probably easiest.

In order to use the elimination method, one of the variables in an equation must be opposite to its corresponding variable in the other equation.
6x+6y=57
4x+3y=33 Multiply this equation by -2. This gets you -8x-6y=-66.

So now, you have:
6x+6y=57
-8x-6y=-9

Add these two equations together: 6x-8x= -2x, the two Y's cancel each other out, and 57-66=-9. So now you have -2x=-9, which means x= 4.5

Now plug 4.5 in for x into one of those equations. Let's use the equation 6x+6y=57.

6(4.5)+6y=57
-30=-6y
5=Y

Values of X is 4.5, value of Y is 5. This means that roses cost $4.5 and shrubs are $5. Hope that helped!

Answer 2

1. 4x + 3y = 33
33-4x = 3y
11- (4/3)x = y

2. 6x + 6y = 57
x+y = 57/6
y=(57/6) - x

Equate the two Ys and solve.

Answer 3

4x + 3y = 33
6x + 6y = 57

- 8x - 6y = - 66
6x + 6y = 57--------Add
-2x = - 9
x = 4.5

18 + 3y = 33
3y = 15
y = 5

Roses cost £ 4.50 each
Shrubs cost £ 5.00 each