[latex]\\begin{array}{l}\\text{ }2x+3y - 6z=1\\hfill \\\\ -4x - 6y+12z=-2\\hfill \\\\ \\text{ }x+2y+5z=10\\hfill \\end{array}[\/latex]<\/p>\r\n5.\u00a0Every system of equations can be solved graphically, by substitution, and by addition. However, systems of three equations become very complex to solve graphically so other methods are usually preferable.\r\n\r\n7. No\r\n\r\n9.\u00a0Yes\r\n\r\n11.\u00a0[latex]\\left(-1,4,2\\right)[\/latex]\r\n\r\n13.\u00a0[latex]\\left(-\\frac{85}{107},\\frac{312}{107},\\frac{191}{107}\\right)[\/latex]\r\n\r\n15.\u00a0[latex]\\left(1,\\frac{1}{2},0\\right)[\/latex]\r\n\r\n17.\u00a0[latex]\\left(4,-6,1\\right)[\/latex]\r\n\r\n19.\u00a0[latex]\\left(x,\\frac{1}{27}\\left(65 - 16x\\right),\\frac{x+28}{27}\\right)[\/latex]\r\n\r\n21.\u00a0[latex]\\left(-\\frac{45}{13},\\frac{17}{13},-2\\right)[\/latex]\r\n\r\n23.\u00a0No solutions exist\r\n\r\n25.\u00a0[latex]\\left(0,0,0\\right)[\/latex]\r\n\r\n27.\u00a0[latex]\\left(\\frac{4}{7},-\\frac{1}{7},-\\frac{3}{7}\\right)[\/latex]\r\n\r\n29.\u00a0[latex]\\left(7,20,16\\right)[\/latex]\r\n\r\n31.\u00a0[latex]\\left(-6,2,1\\right)[\/latex]\r\n\r\n33.\u00a0[latex]\\left(5,12,15\\right)[\/latex]\r\n\r\n35.\u00a0[latex]\\left(-5,-5,-5\\right)[\/latex]\r\n\r\n37.\u00a0[latex]\\left(10,10,10\\right)[\/latex]\r\n\r\n39.\u00a0[latex]\\left(\\frac{1}{2},\\frac{1}{5},\\frac{4}{5}\\right)[\/latex]\r\n\r\n41.\u00a0[latex]\\left(\\frac{1}{2},\\frac{2}{5},\\frac{4}{5}\\right)[\/latex]\r\n\r\n43.\u00a0[latex]\\left(2,0,0\\right)[\/latex]\r\n\r\n45.\u00a0[latex]\\left(1,1,1\\right)[\/latex]\r\n\r\n47.\u00a0[latex]\\left(\\frac{128}{557},\\frac{23}{557},\\frac{28}{557}\\right)[\/latex]\r\n\r\n49.\u00a0[latex]\\left(6,-1,0\\right)[\/latex]","rendered":"
1.\u00a0No, there can be only one, zero, or infinitely many solutions.<\/p>\n
3.\u00a0Not necessarily. There could be zero, one, or infinitely many solutions. For example, [latex]\\left(0,0,0\\right)[\/latex] is not a solution to the system below, but that does not mean that it has no solution.<\/p>\n
[latex]\\begin{array}{l}\\text{ }2x+3y - 6z=1\\hfill \\\\ -4x - 6y+12z=-2\\hfill \\\\ \\text{ }x+2y+5z=10\\hfill \\end{array}[\/latex]<\/p>\n
5.\u00a0Every system of equations can be solved graphically, by substitution, and by addition. However, systems of three equations become very complex to solve graphically so other methods are usually preferable.<\/p>\n
7. No<\/p>\n
9.\u00a0Yes<\/p>\n
11.\u00a0[latex]\\left(-1,4,2\\right)[\/latex]<\/p>\n
13.\u00a0[latex]\\left(-\\frac{85}{107},\\frac{312}{107},\\frac{191}{107}\\right)[\/latex]<\/p>\n
15.\u00a0[latex]\\left(1,\\frac{1}{2},0\\right)[\/latex]<\/p>\n
17.\u00a0[latex]\\left(4,-6,1\\right)[\/latex]<\/p>\n
19.\u00a0[latex]\\left(x,\\frac{1}{27}\\left(65 - 16x\\right),\\frac{x+28}{27}\\right)[\/latex]<\/p>\n
21.\u00a0[latex]\\left(-\\frac{45}{13},\\frac{17}{13},-2\\right)[\/latex]<\/p>\n
23.\u00a0No solutions exist<\/p>\n
25.\u00a0[latex]\\left(0,0,0\\right)[\/latex]<\/p>\n
27.\u00a0[latex]\\left(\\frac{4}{7},-\\frac{1}{7},-\\frac{3}{7}\\right)[\/latex]<\/p>\n
29.\u00a0[latex]\\left(7,20,16\\right)[\/latex]<\/p>\n
31.\u00a0[latex]\\left(-6,2,1\\right)[\/latex]<\/p>\n
33.\u00a0[latex]\\left(5,12,15\\right)[\/latex]<\/p>\n
35.\u00a0[latex]\\left(-5,-5,-5\\right)[\/latex]<\/p>\n
37.\u00a0[latex]\\left(10,10,10\\right)[\/latex]<\/p>\n
39.\u00a0[latex]\\left(\\frac{1}{2},\\frac{1}{5},\\frac{4}{5}\\right)[\/latex]<\/p>\n
41.\u00a0[latex]\\left(\\frac{1}{2},\\frac{2}{5},\\frac{4}{5}\\right)[\/latex]<\/p>\n
43.\u00a0[latex]\\left(2,0,0\\right)[\/latex]<\/p>\n
45.\u00a0[latex]\\left(1,1,1\\right)[\/latex]<\/p>\n
47.\u00a0[latex]\\left(\\frac{128}{557},\\frac{23}{557},\\frac{28}{557}\\right)[\/latex]<\/p>\n
49.\u00a0[latex]\\left(6,-1,0\\right)[\/latex]<\/p>\n\n\t\t\t Candela Citations<\/h3>\n\t\t\t\t\t