Simultaneous equations

Solve algebraically the simultaneous equations x + 7 y = 14 3 x – y = 9

Solve algebraically the simultaneous equations

3 x + y = 2

C is a circle with centre (0, 0) The straight line with equation 3 x – 2 y = 52 is the tangent to C at the point P. Find the coordinates of P.

1 cup of tea and 1 cup of coffee cost £4.50 3 cups of tea and 1 cup of coffee cost £8.50 Work out the total cost of 4 cups of tea and 3 cups of coffee. You must show all your working.

Use algebra to solve the simultaneous equations 4 x – 5 y = 20 6 x + 7 y = –57 You must show all your working.

OBCD is a rectangle. DCE is a straight line.

B has coordinates (2, −4) E has coordinates (12, −6.5) Work out the coordinates of D. You must show all your working.

Solve the simultaneous equations

y + 2 x = 7 Give your solutions correct to 3 significant figures.

Solve the simultaneous equations 5 x – 2 y = 23 2 x – 3 y = 18

On the grid, draw the graph of x² + y² = 169

Use your graph to find estimates for the solutions of the simultaneous equations

2 y = 3 x

Solve the simultaneous equations 3 x + y = −4.5 4 x + 3 y = −3.5

Use these graphs to solve the simultaneous equations 2 – 2 y = x 2 y = 3 x – 22

Use these graphs to solve the simultaneous equations 2 – 2 y = x 2 y = 3 x – 22

Use algebra to solve the simultaneous equations 2 x + 6 y = 5 3 x – 4 y = –12

Solve the simultaneous equations 5 x + 2 y = 11 4 x + 3 y = 6

Solve the simultaneous equations 5 x + 2 y = 27 6 x + 4 y = 28

L is the straight line with equation y = 2x − 5 C is a graph with equation y² = 6x² − 25x − 8 Using algebra, find the coordinates of the points of intersection of L and C. You must show all your working.

20The diagram shows the graph of x² + y² = 30.25

Use the graph to find estimates for the solutions of the simultaneous equations x² + y² = 30.25 y – 2x = 1

16The curve C has equation y = x² + 3x – 3 The line L has equation y – 5x + 4 = 0 Show, algebraically, that C and L have exactly one point in common.

Use these graphs to solve the simultaneous equations 5 x − 9 y = −46 y = − 2 x

Use this graph to find estimates for the solutions of the quadratic equation x² − 4x + 2 = 0

Use these graphs to solve the simultaneous equations 5 x − 9 y = −46 y = − 2 x

Use this graph to find estimates for the solutions of the quadratic equation x² − 4x + 2 = 0

grid below.

Using the graphs, find estimates of the solutions of the simultaneous equations

There are only red counters and g green counters in a bag. A counter is taken at random from the bag. The probability that the counter is green is The counter is put back in the bag. 2 more red counters and 3 more green counters are put in the bag. A counter is taken at random from the bag. The probability that the counter is green is Find the number of red counters and the number of green counters that were in the bag originally.

Solve the simultaneous equations

Solve algebraically the simultaneous equations

Solve the simultaneous equations

5 x + y = 21 x − 3 y = 9

Solve the simultaneous equations

5 x + y = 21 x − 3 y = 9

p and q are two numbers such that p q

When you subtract 5 from p and subtract 5 from q the answers are in the ratio 5: 1 When you add 20 to p and add 20 to q the answers are in the ratio 5: 2

Find the ratio p: q Give your answer in its simplest form.

The straight line L₁ passes through the points with coordinates (4, 6) and (12, 2) The straight line L₂ passes through the origin and has gradient −3

The lines L₁ and L₂ intersect at point P.

Find the coordinates of P.

Solve algebraically the simultaneous equations

x + 2 y = 1

On the grid, draw the graph of x² + y² = 12.25

Hence find estimates for the solutions of the simultaneous equations

2 x + y = 1

The nth term of a sequence is given by an² + bn where a and b are integers.

The 2nd term of the sequence is –2 The 4th term of the sequence is 12

Find the 6th term of the sequence.

Here are the first five terms of a different quadratic sequence.

0 2 6 12 20

Find an expression, in terms of n, for the n th term of this sequence.

3 teas and 2 coffees have a total cost of £7.80 5 teas and 4 coffees have a total cost of £14.20

Work out the cost of one tea and the cost of one coffee.

The functions f and g are such that

g(3) = 20 and f⁻¹

Find the value of a and the value of b.

Solve the simultaneous equations

x + 3 y = 12 5 x − y = 4

Solve the simultaneous equations

3 x + y = –4 3 x – 4 y = 6

Solve the simultaneous equations

3 x + y = –4 3 x – 4 y = 6