Checkpoint 8.28. Pause and Reflect.
What is a solution to a 3x3 linear system?
\(-2x\) | \(-\) | \(4y\) | \(+\) | \(6z\) | \(=\) | \(8\) | \(\hphantom{blank}\) | \(-2\times (1)\) |
\(2x\) | \(-\) | \(y\) | \(+\) | \(z\) | \(=\) | \(3\) | \(\) | \((2)\) |
\(\) | \(\) | \(-5y\) | \(+\) | \(7z\) | \(=\) | \(11\) | \(\) | \((4)\) |
\(-3x\) | \(-\) | \(6y\) | \(+\) | \(9z\) | \(=\) | \(12\) | \(\hphantom{blank}\) | \(-3\times (1)\) |
\(3x\) | \(+\) | \(2y\) | \(+\) | \(z\) | \(=\) | \(10\) | \(\) | \((3)\) |
\(\) | \(\) | \(-4y\) | \(+\) | \(10z\) | \(=\) | \(22\) | \(\) | \((5)\) |
\(-20y\) | \(+\) | \(28z\) | \(=\) | \(44\) | \(\hphantom{blank}\) | \(4\times (4)\) |
\(20y\) | \(-\) | \(50z\) | \(=\) | \(-110\) | \(\) | \(-5\times (5)\) |
\(\) | \(\) | \(-22z\) | \(=\) | \(-66\) | \(\) | \((6)\) |
\(x\) | \(+\) | \(2y\) | \(-\) | \(z\) | \(=\) | \(-3\) | \(\hphantom{blank}\) | \((1)\) |
\(x\) | \(-\) | \(3y\) | \(+\) | \(z\) | \(=\) | \(6\) | \(\) | \((2\text{a})\) |
\(2x\) | \(-\) | \(y\) | \(\) | \(\) | \(=\) | \(3\) | \(\) | \((4)\) |
\(2x\) | \(+\) | \(4y\) | \(-\) | \(2z\) | \(=\) | \(-6\) | \(\hphantom{blank}\) | \((1\text{a})\) |
\(2x\) | \(+\) | \(y\) | \(+\) | \(2z\) | \(=\) | \(5\) | \(\) | \((3\text{a})\) |
\(4x\) | \(+\) | \(5y\) | \(\) | \(\) | \(=\) | \(-1\) | \(\) | \((5)\) |
\(-6x\) | \(-\) | \(2y\) | \(+\) | \(4z\) | \(=\) | \(-2\) |
\(6x\) | \(+\) | \(2y\) | \(-\) | \(4z\) | \(=\) | \(5\) |
\(0x\) | \(+\) | \(0y\) | \(+\) | \(0z\) | \(=\) | \(3\) |
\(-2x\) | \(+\) | \(6y\) | \(-\) | \(2z\) | \(=\) | \(-4\) |
\(2x\) | \(-\) | \(6y\) | \(+\) | \(2z\) | \(=\) | \(4\) |
\(0x\) | \(+\) | \(0y\) | \(+\) | \(0z\) | \(=\) | \(0\) |
\(x\) | \(+\) | \(y\) | \(-\) | \(z\) | \(=\) | \(-20\) | \((2)\) | |
\(x\) | \(+\) | \(y\) | \(+\) | \(2z\) | \(=\) | \(4\) | \((3)\) | |
\(2x\) | \(+\) | \(2y\) | \(\) | \(\) | \(=\) | \(160\) | \((4)\) |
\(x\) | \(-\) | \(2y\) | \(=\) | \(-4\) | \((1)\) | |
\(2x\) | \(+\) | \(2y\) | \(=\) | \(160\) | \((4)\) | |
\(3x\) | \(\) | \(\) | \(=\) | \(156\) | \((5)\) |
Number of two-drawer cabinets: | \(x\) |
Number of four-drawer cabinets: | \(y\) |
Number of horizontal cabinets: | \(z\) |
\(\displaystyle{}\) | 2-Drawer | 4-Drawer | Horizontal | Total available |
Assembly | ||||
Painting | ||||
Finishing |
Assembly time: | \((1)\) | |
Painting time: | \((2)\) | |
Finishing time: | \((3)\) |
Assembly time: | \(3*x+5*y+4*z = 500\) | \((1)\) |
Painting time: | \(x+1.5*y+z = 150\) | \((2)\) |
Finishing time: | \(x+2*y+3*z = 230\) | \((3)\) |