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Systems of Equations (Easy)

AMC 10 Q1–8 depth — contest entry, not school drills.

Easy Medium Hard AIME / USAJMO / AMO

Systems of Equations: core idea

Substitution.

Example problem: hint and answer

Solve $x+y=10$ , $x-y=2$ for $x$ .

Hint: Substitute the known expression or add equations. Answer: 6.

Practice (9 problems — type your answers)

1. Solve $x+y=7$ , $y=3$ for $x$ .
2. If $2x=14$ and $x+y=10$ , find $y$ .
3. Solve $x+y=9$ , $x=2y$ for $y$ .
4. Solve $3x+y=11$ , $x=2$ for $y$ .
5. Find $x+y$ if $x=4$ and $y=-1$ .
6. Solve $x-y=5$ , $y=2$ for $x$ .
7. Solve $x+y=8$ , $x-y=0$ for $x$ .
8. If $x=3y$ and $x+y=16$ , find $y$ .
9. Solve $2x+y=9$ , $x=3$ for $y$ .

Systems of Equations Practice Problems — Easy