4.7: Systems of Equations- Answers to the Homework Exercises
- Page ID
- 45050
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Graphing
- No
- Yes
- \((-1,2)\)
- No Solution
- \((-3,-1)\)
- \((1,-3)\)
- \((2,-2)\)
- \((3,2)\)
- \((-1,-2)\)
- \((4,-2)\)
- \((-3,1)\)
- \((4,4)\)
- \((4,-4)\)
- No Solution
- \((2,-1)\)
- \((2,3)\)
- \((-3,1)\)
The Substitution Method
- \((1, −3)\); consistent; independent
- \((−1, −2)\); consistent; independent
- \((3, 3)\); consistent; independent
- \((−2, −6)\); consistent; independent
- \((−1, 8)\); consistent; independent
- \((1, 7)\); consistent; independent
- \((1, 3)\); consistent; independent
- \((4, −3)\); consistent; independent
- \((0, 3)\); consistent; independent
- \((−4, −1)\); consistent; independent
- \((−3, 3)\); consistent; independent
- \((−1, 0)\); consistent; independent
- \((8, −8)\); consistent; independent
- \((1, −3)\); consistent; independent
- \((−4, 3)\); consistent; independent
- \((0, 2)\); consistent; independent
- \((4, −2)\); consistent; independent
- \((−4, 8)\); consistent; independent
- \((1, −4)\); consistent; independent
- \((2, 5)\); consistent; independent
The Addition Method
- \((−2, 4)\); consistent; independent
- No solution; inconsistent
- \((−3, −5)\); consistent; independent
- \((0, 4)\); consistent; independent
- \((4, 6)\); consistent; independent
- \((0, −4)\); consistent; independent
- \((−1, −2)\); consistent; independent
- \((−8, 9)\); consistent; independent
- \((0, 0)\); consistent; independent
- Infinite number of solutions; consistent; dependent
- \((2, −2)\); consistent; independent
- \((1, −2)\); consistent; independent
- \((0, 3)\); consistent; independent
- \((1, 2)\); consistent; independent
- \((2, −2)\); consistent; independent
- \((−3, 0)\); consistent; independent
- \((−1, 1)\); consistent; independent
Applications with Systems of Equations
- \(236\) adult, \(342\) child
- \(130\) adults, \(70\) students
- \(73\) hotdogs, \(58\) hamburgers
- \($12,500 \:@\: 12\%\); \($14,500\: @\: 13\%\)
- \($2,500\: @\: 10\%\); \($6,500\: @\: 12\%\)
- \($4,100\: @\: 9.5\%\); \($5,900\: @\: 11\%\)
- \($1,600\: @\: 4\%\); \($2,400\: @\: 8\%\)
- \($3,500\: @\: 6\%\); \($5,000\: @\: 3.5\%\)
- \($6,500\: @\: 8\%\); \($8,500\: @\: 11\%\)
- \($3,000\: @\: 4.25\%\); \($3,000\: @\: 5.75\%\)
- \($7,500\: @\: 6.8\%\); \($3,500\: @\: 8.2\%\)
- \($5,000\: @\: 12\%\); \($11,000\: @\: 8\%\)
- \(30,\: 70\)
- \(40,\: 110\)
- \(100,\: 200\)
- \(10,\: 5\)
- \(21,\: 49\)
- \(2,\: 3\)
- \(1.5,\: 3.5\)
- \(55,\: 20\)
- \(35,\: 63\)
- \(1.2\)
- \(10\)
- \(75\)
- \(63\) mph in still water; \(9\) mph current’s rate
- \(5\) mph in still water; \(1\) mph current’s rate
- \(\frac{783}{8}\) mph in still air; \(\frac{113}{8}\) mph wind’s rate
- \(35\) mph in still air; \(5\) mph wind’s rate
Systems of Three Linear Equations in Three Variables
- \((1, −1, 2)\); consistent; independent
- \((−2, −1, 4)\); consistent; independent
- \((0, 0, 0)\); consistent; independent
- \((0, 0, 0)\); consistent; independent
- \((1, 2, 3)\); consistent; independent
- \((10, 2, 3)\); consistent; independent
- \((3, −2, 1)\); consistent; independent
- \(\{(x, y, z)|x + y − z = 0\}\); consistent; dependent
- \(\{(x, y, z)|4x + 12y + 16z = 4\}\); consistent; dependent
- \(\{(p, q, r)|p + q + r = 1\}\); consistent; dependent
- no solution; inconsistent
- \((2, 3, 1)\); consistent; independent
- \((−25, 18, −25)\); consistent; independent
- \((1, 2, 4)\); consistent; independent
- \((1, −3, −2, −1)\); consistent; independent
- \((7, 4, 5, 6)\); consistent; independent
Systems of Two Linear Inequalities in Two Variables
- yes, no, yes
- yes, no, no