# Thread: simultaneous equations

1. ## simultaneous equations

Consider the simultaneous equations
mx + 2y = 8
4x - (2-m)y = 2m
a) Find the values of m for which there are:
i) no solutions
ii) infinitely many solutions

please explain how to do this, i am very confused, thank you.

answer:
i) m = -2
ii) m = 4

2. Originally Posted by emma
mx + 2y = 8
4x - (2-m)y = 2m

You can turn these equations into the form $y=mx+c$ giving
$mx + 2y = 8 \implies y=\frac{-m}{2}x+4$

and

$
4x - (2-m)y = 2m \implies y = \frac{-4}{2-m}x+\frac{2m}{2-m}
$

Now equating coeffecients of x you solve for

$\frac{-m}{2} = \frac{-4}{2-m}$

Cross multiplying

$-8 = -2m+m^2$

solving the quadratic gives

$m = -2 , 4$

So which one gives no solutions and which infinitely many solutions?

The hint here is where the constant term in each equation is equal, this will yield infinitely many solutions