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
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
You can turn these equations into the form $\displaystyle y=mx+c$ giving
$\displaystyle mx + 2y = 8 \implies y=\frac{-m}{2}x+4$
and
$\displaystyle
4x - (2-m)y = 2m \implies y = \frac{-4}{2-m}x+\frac{2m}{2-m}
$
Now equating coeffecients of x you solve for
$\displaystyle \frac{-m}{2} = \frac{-4}{2-m}$
Cross multiplying
$\displaystyle -8 = -2m+m^2$
solving the quadratic gives
$\displaystyle m = -2 , 4$
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