1. Simultaneous equations

If (2,1) is a solution of the simultaneous equations
x(square) + xy + ay = b
2ax + 3y = b

find the value of a and b.
Find also the other solution.
I was able to find out
a=1
b=7
But not the other solution.
the answer is supposed to be:
x=-7 and y=7

2. Originally Posted by Ilsa
If (2,1) is a solution of the simultaneous equations
x(square) + xy + ay = b
2ax + 3y = b

find the value of a and b.
Find also the other solution.
I was able to find out
a=1
b=7 <====== OK
But not the other solution.
the answer is supposed to be:
x=-7 and y=7
1. Plug in the values of a and b into the two equations:

$\displaystyle \left|\begin{array}{rcl}x^2+xy+y&=&7\\2x+3y&=&7\en d{array}\right.$

2. Determine x from the 2nd equation: $\displaystyle x= -\frac32 y+\frac72$

3. Now replace x in the 1st equation by $\displaystyle -\frac32 y+\frac72$ and solve for y:

$\displaystyle \left(-\frac32 y+\frac72\right)^2+\left(-\frac32 y+\frac72\right) \cdot y + y = 7$

4. Plug in the value of y into the equation at 2. to get the value of x.