Question

How many solutions are there to the following system of equations 4x – 8y = 0 and –3x + 8y = –7?

Answer 1

One : `(-7,-7/2)`.

Explanation:

Adding the two equations

`4x-8y=0`
`-3x+8y=-7`

we get
`x=-7`

Substituting this value back in the first equation, we get
`y=-7/2`

Thus, the pair of equations have one solution

It is easy to understand this result in terms of graphs. Graphically the two equations represent straight lines of different slopes. Thus, they must intersect at exactly one point - hence the single solution.