Linear simultaneous equations

1. In this question you must show all stages of your working. Solutions relying entirely on calculator technology are not acceptable.

A rectangular sports pitch has length \(x\) metres and width \(y\) metres, where \(x > y\) Given that the perimeter of the pitch is 350 m ,

1. write down an equation linking \(x\) and \(y\) Given also that the area of the pitch is \(7350 \mathrm {~m} ^ { 2 }\)
2. write down a second equation linking \(x\) and \(y\)
3. hence find the value of \(x\) and the value of \(y\)

4 Find, algebraically, the coordinates of the point of intersection of the lines \(y = 2 x - 5\) and \(6 x + 2 y = 7\).

4 Find the coordinates of the point of intersection of the lines \(x + 2 y = 5\) and \(y = 5 x - 1\).

8 Find the coordinates of the point of intersection of the lines \(x + 2 y = 5\) and \(y = 5 x - 1\).

2 Find the coordinates of the point of intersection of the lines \(2 x + 3 y = 12\) and \(y = 7 - 3 x\).

2 Alex is comparing the cost of mobile phone contracts. Contract \(\boldsymbol { A }\) has a set-up cost of \(\pounds 40\) and then costs 4 p per minute. Contract \(\boldsymbol { B }\) has no set-up cost, does not charge for the first 100 minutes and then costs 6 p per minute.

1. Find an expression for the cost of each of the contracts in terms of \(m\), where \(m\) is the number of minutes for which the phone is used and \(m > 100\).
2. Hence find the value of \(m\) for which both contracts would cost the same.

1 Find the coordinates of the point of intersection of the lines \(y = 3 x - 2\) and \(x + 2 y = 10\).

6 Solve the simultaneous equations $$x + y = 1 , \quad x ^ { 2 } - 2 x y + y ^ { 2 } = 9 .$$

Find the coordinates of the point of intersection of the lines \(y = 3x + 1\) and \(x + 3y = 6\). [3]

Find the coordinates of the point of intersection of the lines \(y = 3x - 2\) and \(x + 3y = 1\). [4]

Find, algebraically, the coordinates of the point of intersection of the lines \(y = 2x - 5\) and \(6x + 2y = 7\). [4]