Simultaneous Equations

$$\begin{aligned} 2x + 3y &= 4\\ 3x - y &= 17 \end{aligned}$$

$$\begin{aligned} 3x - 4y &= 1\\ 5x - 3y &= 9 \end{aligned}$$

Solve algebraically the system of equations

$$\begin{aligned} 3x + 2y &= 17 \\ 2x + 5y &= 4 \end{aligned}$$

Solve, algebraically, the system of equations

$$\begin{aligned} 4x + 5y &= -3 \\ 6x - 2y &= 5 \end{aligned}$$

Solve, algebraically, the system of equations

$$\begin{aligned} 5c + 2d &= \ 4\\ 4c - 3d &= 17 \end{aligned}$$

Solve, algebraically, the system of equations

$$\begin{aligned} 2x + 3y &= 8 \\ 5x + 2y &= -2 \end{aligned}$$

Solve, algebraically, the system of equations

$$\begin{aligned} 2p - 7r &= 11 \\ 3p + 2r &= 4 \end{aligned}$$

Charlie is making costumes for a school show.

(a)  One day he made 2 cloaks and 3 dresses. The total amount of material he used was 9.6 square metres. Write down an equation to illustrate this information.

(b)  The following day Charlie made 3 cloaks and 4 dresses. The total amount of material he used was 13.3 square metres. Write down an equation to illustrate this information.

(c)  Calculate the amount of material required to make one cloak and the amount of material required to make one dress.

John bought 7 bags of cement and 3 bags of gravel.
The total weight of these bags was 215 kilograms.
(a)  Write down an equation to illustrate this information.

Shona bought 5 bags of cement and 4 bags of gravel.
The total weight of her bags was 200 kilograms.
(b)  Write down an equation to illustrate this information.

(c)  Calculate the weight of one bag of cement and the weight of one bag of gravel.

Moira buys 4 mangoes and 3 apples at a fruit shop.
The total cost is £4.25.
(a)  Write down an equation to illustrate this information.

Sami buys 5 mangoes and 2 apples in the same fruit shop.
The total cost is £4.70.
(b)  Write down an equation to illustrate this information.

(c)  Calculate, algebraically, the cost of a mango and the cost of an apple.

On Bob's lorry there are 7 stacks of paving slabs and 3 stacks of edging blocks. The total weight is 2400 kg.
(a)  Write down an equation in $\displaystyle p$ and $\displaystyle e$ to illustrate this information.

Imran has 3 stacks of paving slabs and 4 stacks of edging blocks. The total weight is 1300 kg.
(b)  Write down an equation in $\displaystyle p$ and $\displaystyle e$ to illustrate this information.

Beth has 6 stacks of paving slabs and 5 stacks of edging blocks.
(c)  Calculate the total weight of the stacks on Beth's lorry.

For a hobby, Alex makes cups and plates.
To make 5 cups and 6 plates, it takes Alex 45 minutes.
Let c be the number of minutes Alex takes to make a cup and p be the number of minutes Alex takes to make a plate.
(a)  Write down an equation in c and p to illustrate this information.
To make 7 cups and 4 plates, it takes Alex 52 minutes.
(b)  Write down an equation in c and p to illustrate this information.
(c)  Calculate, algebraically, the total number of minutes it will take Alex to make 10 cups and 8 plates.