Answer:
20) [tex]\displaystyle [4, 1][/tex]
19) [tex]\displaystyle [-5, 1][/tex]
18) [tex]\displaystyle [3, 2][/tex]
17) [tex]\displaystyle [-2, 1][/tex]
16) [tex]\displaystyle [7, 6][/tex]
15) [tex]\displaystyle [-3, 2][/tex]
14) [tex]\displaystyle [-3, -2][/tex]
13) [tex]\displaystyle NO\:SOLUTION[/tex]
12) [tex]\displaystyle [-4, -1][/tex]
11) [tex]\displaystyle [7, -2][/tex]
Step-by-step explanation:
20) {−2x - y = −9
{5x - 2y = 18
⅖[5x - 2y = 18]
{−2x - y = −9
{2x - ⅘y = 7⅕ >> New Equation
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[tex]\displaystyle \frac{-1\frac{4}{5}y}{-1\frac{4}{5}} = \frac{-1\frac{4}{5}}{-1\frac{4}{5}}[/tex]
[tex]\displaystyle y = 1[/tex][Plug this back into both equations above to get the x-coordinate of 4]; [tex]\displaystyle 4 = x[/tex]
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19) {−5x - 8y = 17
{2x - 7y = −17
−⅞[−5x - 8y = 17]
{4⅜x + 7y = −14⅞ >> New Equation
{2x - 7y = −17
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[tex]\displaystyle \frac{6\frac{3}{8}x}{6\frac{3}{8}} = \frac{-31\frac{7}{8}}{6\frac{3}{8}}[/tex]
[tex]\displaystyle x = -5[/tex][Plug this back into both equations above to get the y-coordinate of 1]; [tex]\displaystyle 1 = y[/tex]
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18) {−2x + 6y = 6
{−7x + 8y = −5
−¾[−7x + 8y = −5]
{−2x + 6y = 6
{5¼x - 6y = 3¾ >> New Equation
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[tex]\displaystyle \frac{3\frac{1}{4}x}{3\frac{1}{4}} = \frac{9\frac{3}{4}}{3\frac{1}{4}}[/tex]
[tex]\displaystyle x = 3[/tex][Plug this back into both equations above to get the y-coordinate of 2]; [tex]\displaystyle 2 = y[/tex]
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17) {−3x - 4y = 2
{3x + 3y = −3
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[tex]\displaystyle \frac{-y}{-1} = \frac{-1}{-1}[/tex]
[tex]\displaystyle y = 1[/tex][Plug this back into both equations above to get the x-coordinate of −2]; [tex]\displaystyle -2 = x[/tex]
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16) {2x + y = 20
{6x - 5y = 12
−⅓[6x - 5y = 12]
{2x + y = 20
{−2x + 1⅔y = −4 >> New Equation
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[tex]\displaystyle \frac{2\frac{2}{3}y}{2\frac{2}{3}} = \frac{16}{2\frac{2}{3}}[/tex]
[tex]\displaystyle y = 6[/tex][Plug this back into both equations above to get the x-coordinate of 7]; [tex]\displaystyle 7 = x[/tex]
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15) {6x + 6y = −6
{5x + y = −13
−⅚[6x + 6y = −6]
{−5x - 5y = 5 >> New Equation
{5x + y = −13
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[tex]\displaystyle \frac{-4y}{-4} = \frac{-8}{-4}[/tex]
[tex]\displaystyle y = 2[/tex][Plug this back into both equations above to get the x-coordinate of −3]; [tex]\displaystyle -3 = x[/tex]
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14) {−3x + 3y = 3
{−5x + y = 13
−⅓[−3x + 3y = 3]
{x - y = −1 >> New Equation
{−5x + y = 13
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[tex]\displaystyle \frac{-4x}{-4} = \frac{12}{-4}[/tex]
[tex]\displaystyle x = -3[/tex][Plug this back into both equations above to get the y-coordinate of −2]; [tex]\displaystyle -2 = y[/tex]
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13) {−3x + 3y = 4
{−x + y = 3
−⅓[−3x + 3y = 4]
{x - y = −1⅓ >> New Equation
{−x + y = 3
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[tex]\displaystyle 1\frac{2}{3} ≠ 0; NO\:SOLUTION[/tex]
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12) {−3x - 8y = 20
{−5x + y = 19
⅛[−3x - 8y = 20]
{−⅜x - y = 2½ >> New Equation
{−5x + y = 19
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[tex]\displaystyle \frac{-5\frac{3}{8}x}{-5\frac{3}{8}} = \frac{21\frac{1}{2}}{-5\frac{3}{8}}[/tex]
[tex]\displaystyle x = -4[/tex][Plug this back into both equations above to get the y-coordinate of −1]; [tex]\displaystyle -1 = y[/tex]
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11) {x + 3y = 1
{−3x - 3y = −15
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[tex]\displaystyle \frac{-2x}{-2} = \frac{-14}{-2}[/tex]
[tex]\displaystyle x = 7[/tex][Plug this back into both equations above to get the y-coordinate of −2]; [tex]\displaystyle -2 = y[/tex]
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