Simultaneous equations

Solve the simultaneous equations

2 x + 5 y = 18 2 x + y = 6

A curve has the equation y = x² + 4x – 4 A straight line has the equation y = 3 x – 2

Work out the two points of intersection of the curve and the straight line.

4 chocolate bars and 3 packets of mints cost £4.70 5 chocolate bars and 1 packet of mints cost £4.50

Work out the cost of a chocolate bar and the cost of a packet of mints.

Solve these simultaneous equations.

7 x + 2 y = 100 3 x + 2 y = 48

Solve these simultaneous equations.

7 x + 2 y = 100 3 x + 2 y = 48

Solve the simultaneous equations 2 x – 5 y = 13 3 x + 4 y = 8

Here are two simultaneous equations.

and y = 3 x + d There is a solution when x = 5 Work out the value of c + d

f(x) = cx + d f(4) = 7 f(10) = 22 Work out the values of c and d.

24 (b) g(x) = 2x and h(x) =

Circle the expression for hg(x)

Solve the simultaneous equations 2 x + 4 y = – 9 2 y = 4 x – 7

Solve the simultaneous equations 7 x + 2 y = 36 3 x + 2 y = 16

Solve the simultaneous equations 7 x + 2 y = 36 3 x + 2 y = 16

Solve the simultaneous equations 2 x + 3 y = 5 p y = 2 x + p where p is a constant. Give your answers in terms of p in their simplest form.

In a chess club, there are x boys and y girls.

If 5 more boys and 8 more girls join, there would be half as many boys as girls. Show that y = 2 x + 2

If instead, 10 more boys and 1 more girl join, there would be the same number of boys and girls. Work out x and y.

x =

y =

The line y = 3x + p and the circle x² + y² = 53 intersect at points A and B. p is a positive integer.

Show that the x-coordinates of points A and B satisfy the equation

The coordinates of A are (2, 7) Work out the coordinates of B. You must show your working.

A curve has equation y = 4x² + 5x + 3 A line has equation y = x + 2 Show that the curve and the line have exactly one point of intersection. Do not use a graphical method.

Solve the simultaneous equations. 2 x + y = 18

Solve the simultaneous equations.

2 x + y = 18