Tier 1 · algebra

2x2 Systems

Reference card for 2-variable system methods.

Files (1)

SYS2X2.py475 bytes

def p(s):print(s)
def o1():
 p("=SUB=")
 p("SOLVE 1ST")
 p("FOR 1 VAR")
 p("SUB INTO 2ND")
 p("SOLVE REM VAR")
def o2():
 p("=ELIM=")
 p("MULTIPLY EQS")
 p("MATCH COEFS")
 p("ADD TO ELIM")
 p("SOLVE BACK")
def o3():
 p("=GRAPH=")
 p("PLOT BOTH")
 p("FIND INT PT")
 p("(x,y)=SOL")
def menu():
 while True:
  p("=SYS 2X2=")
  p("1:SUB")
  p("2:ELIM")
  p("3:GRAPH")
  p("0:EXIT")
  c=input("?>")
  if c=="1":o1()
  elif c=="2":o2()
  elif c=="3":o3()
  elif c=="0":break
menu()

How to use it

Reference card for the three ways to solve a 2-variable system:

1:SUB — substitution: solve one equation for a variable, sub into the other.
2:ELIM — elimination: multiply to match a coefficient, add to cancel, solve back.
3:GRAPH — graphical: plot both lines, read off the intersection.
0:EXIT — leave.

Each option prints a 4-line procedure. Pick the method that fits the system: SUB when one equation already isolates a variable, ELIM when coefficients are close, GRAPH when the intersection is at integer coordinates.

Example problem

You're solving 2x + y = 10 and 3x − y = 5 and can't remember which method is fastest.

The y coefficients are already +1 and −1 — perfect for elimination.

Run SYS2X2.
Pick 2:ELIM.
Screen shows: MULTIPLY EQS / MATCH COEFS / ADD TO ELIM / SOLVE BACK.

Apply: add the two equations → 5x = 15 → x = 3. Sub back: 2(3) + y = 10 → y = 4. Solution (3, 4). ✓

TI-84 Plus CE — try before committingoff

TI-84 Plus CE




  (calculator off)

  Press ON to start.

Test cases (2)

ID	Inputs	Expected contains
sub-method	1, 0	SOLVE 1ST
elim-method	2, 0	MULTIPLY