{
  "icon" : "square.grid.3x3",
  "id" : "68DEC6DA-8B59-5E2A-B9C5-3094F0319F9E",
  "lines" : [
    {
      "id" : "720C8F1B-BFFF-52E2-AEBF-A4E230F8C31E",
      "source" : "# Two equations"
    },
    {
      "id" : "50430763-262B-5A53-932F-351B1A09D4E0",
      "source" : "\/\/ 2x + y = p and 3x + y = q. Drag p and q."
    },
    {
      "id" : "358D06F6-44CA-542A-82E4-FF3578887EFA",
      "source" : "p = 8 in 0 … 20"
    },
    {
      "id" : "63036F9C-BC47-50C1-BC09-EAA7E3E86749",
      "source" : "q = 11 in 0 … 20"
    },
    {
      "id" : "6090FA00-CD24-5EC4-9454-9418088B0E9C",
      "source" : ""
    },
    {
      "id" : "95601D68-D3EF-5FD1-A3BE-791E0C4605A5",
      "source" : "# Elimination"
    },
    {
      "id" : "0E79AEAD-DA66-5E37-B899-005A6B35CE93",
      "source" : "\/\/ Subtract the first equation from the second: the y terms cancel, leaving x = q - p."
    },
    {
      "id" : "CCB0B8E7-3E22-597A-ADC4-E18241DF980E",
      "source" : "x = (q - p)\/(3 - 2)"
    },
    {
      "id" : "96844FDE-6595-56A6-8912-8BDF93EE2647",
      "source" : ""
    },
    {
      "id" : "38BD6607-2F9B-5C44-9E14-5BB5606A13F3",
      "source" : "# Substitution"
    },
    {
      "id" : "5CE4134A-9949-57B0-B341-BC07E554E759",
      "source" : "\/\/ Solve the first equation for y: y = p - 2x."
    },
    {
      "id" : "9A3AD98C-131E-5D7B-A655-4A1688DAD172",
      "source" : "\/\/ Put that into the second: 3x + (p - 2x) = q, so x = q - p."
    },
    {
      "id" : "11FED0B0-DF4B-5940-B86E-6E2EF2A5F318",
      "source" : "x by substitution = q - p"
    },
    {
      "id" : "64E792BF-B536-5E21-B0B0-4F029DD13EE7",
      "source" : "x by substitution == x"
    },
    {
      "id" : "4D38084D-290C-5A9F-8350-F54E1E07AB6C",
      "source" : "y = p - 2*x"
    },
    {
      "id" : "3DE37A2B-3DA8-56C9-8089-A48E9C644730",
      "source" : ""
    },
    {
      "id" : "64B3F2E2-45AC-50CD-A366-45AF4F906603",
      "source" : "# Check both equations"
    },
    {
      "id" : "4AF571DE-D131-5B5A-8C88-5E235DB51F5D",
      "source" : "2*x + y == p"
    },
    {
      "id" : "11FA549A-0313-55C7-BDA5-407B438D1719",
      "source" : "3*x + y == q"
    }
  ],
  "numberStyle" : {
    "decimal" : ".",
    "grouping" : ",",
    "secondaryGroupSize" : 3
  },
  "title" : "Solving systems two ways"
}