Simultaneous equations Quiz

1. Solve $x+y=7$ and $x-y=3$.

• A. $x=4,\ y=3$
• B. $x=5,\ y=2$
• C. $x=3,\ y=4$
• D. $x=10,\ y=-3$

2. The line $y=x+1$ meets $y=x^2-1$. What are the $x$-coordinates?

• A. $-1,\ 2$
• B. $0,\ 1$
• C. $1,\ -2$
• D. $-1,\ 0$

3. How many solutions has $y=x+5$, $y=x^2+x+5$?

• A. None
• B. Two
• C. Infinitely many
• D. One

4. If $2^x=8$ and $y=x+1$, find $y$.

• A. $3$
• B. $8$
• C. $9$
• D. $4$

5. Which discriminant condition makes $y=mx+1$ a tangent to $y=x^2+x+2$?

• A. $m^2-2m-3<0$
• B. $m^2-2m-3>0$
• C. $m^2-2m-3=0$
• D. $m=0$