# Recent questions tagged system-of-equations

1 vote
1
Consider the pair of equations: $x^{2} – xy – x = 22$ and $y^{2} – xy + y = 34.$ If $x>y,$ then $x – y$ equals $7$ $8$ $6$ $4$
1 vote
2
Let $k$ be a constant. The equations $kx + y= 3$ and $4x + ky= 4$ have a unique solution if and only if $|k| \neq 2$ $|k| = 2$ $k \neq 2$ $k= 2$
1 vote
3
Let $a,b,x,y$ be real numbers such that $a^{2}+b^{2}=25,x^{2}+y^{2}=169$, and $ax+by=65$. If $k=ay-bx$, then $k=0$ $0< k\leq \frac{5}{13}$ $k=\frac{5}{13}$ $k> \frac{5}{13}$
The number of solutions of the equation $2x+y=40$ where both $x$ and $y$ are positive integers and $x\leq y$ is __________
If $x$ and $y$ are integers then the equation $5x + 19y = 64$ has no solution for $x < 300$ and $y < 0$ no solution for $x > 250$ and $y > – 100$ a solution for $250 < x < 300$ a solution for $– 59 < y < – 56$
Which one of the following conditions must $p, q,$ and $r$ satisfy so that the following system of linear simultaneous equations has at least one solution, such that $p+ q + r \neq 0?$ $x+2y-3z=p$ $2x+6y-11z=q$ $x-2y+7z=r$ $5p - 2q - r=0$ $5p + 2q + r=0$ $5p + 2q - r=0$ $5p - 2q + r=0$