Question

Please help me with this​

Answer 1

20)
`\displaystyle [4, 1]`

19)
`\displaystyle [-5, 1]`

18)
`\displaystyle [3, 2]`

17)
`\displaystyle [-2, 1]`

16)
`\displaystyle [7, 6]`

15)
`\displaystyle [-3, 2]`

14)
`\displaystyle [-3, -2]`

13)
`\displaystyle NO\:SOLUTION`

12)
`\displaystyle [-4, -1]`

11)
`\displaystyle [7, -2]`

Explanation:

20) {−2x - y = −9

{5x - 2y = 18

⅖[5x - 2y = 18]

{−2x - y = −9

{2x - ⅘y = 7⅕ >> New Equation

__________

`\displaystyle (-1(4)/(5)y)/(-1(4)/(5)) = (-1(4)/(5))/(-1(4)/(5))`

`\displaystyle y = 1`[Plug this back into both equations above to get the x-coordinate of 4];
`\displaystyle 4 = x`

_______________________________________________

19) {−5x - 8y = 17

{2x - 7y = −17

−⅞[−5x - 8y = 17]

{4⅜x + 7y = −14⅞ >> New Equation

{2x - 7y = −17

_____________

`\displaystyle (6(3)/(8)x)/(6(3)/(8)) = (-31(7)/(8))/(6(3)/(8))`

`\displaystyle x = -5`[Plug this back into both equations above to get the y-coordinate of 1];
`\displaystyle 1 = y`

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18) {−2x + 6y = 6

{−7x + 8y = −5

−¾[−7x + 8y = −5]

{−2x + 6y = 6

{5¼x - 6y = 3¾ >> New Equation

____________

`\displaystyle (3(1)/(4)x)/(3(1)/(4)) = (9(3)/(4))/(3(1)/(4))`

`\displaystyle x = 3`[Plug this back into both equations above to get the y-coordinate of 2];
`\displaystyle 2 = y`

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17) {−3x - 4y = 2

{3x + 3y = −3

__________

`\displaystyle (-y)/(-1) = (-1)/(-1)`

`\displaystyle y = 1`[Plug this back into both equations above to get the x-coordinate of −2];
`\displaystyle -2 = x`

_______________________________________________

16) {2x + y = 20

{6x - 5y = 12

−⅓[6x - 5y = 12]

{2x + y = 20

{−2x + 1⅔y = −4 >> New Equation

____________

`\displaystyle (2(2)/(3)y)/(2(2)/(3)) = (16)/(2(2)/(3))`

`\displaystyle y = 6`[Plug this back into both equations above to get the x-coordinate of 7];
`\displaystyle 7 = x`

_______________________________________________

15) {6x + 6y = −6

{5x + y = −13

−⅚[6x + 6y = −6]

{−5x - 5y = 5 >> New Equation

{5x + y = −13

_________

`\displaystyle (-4y)/(-4) = (-8)/(-4)`

`\displaystyle y = 2`[Plug this back into both equations above to get the x-coordinate of −3];
`\displaystyle -3 = x`

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14) {−3x + 3y = 3

{−5x + y = 13

−⅓[−3x + 3y = 3]

{x - y = −1 >> New Equation

{−5x + y = 13

_________

`\displaystyle (-4x)/(-4) = (12)/(-4)`

`\displaystyle x = -3`[Plug this back into both equations above to get the y-coordinate of −2];
`\displaystyle -2 = y`

_______________________________________________

13) {−3x + 3y = 4

{−x + y = 3

−⅓[−3x + 3y = 4]

{x - y = −1⅓ >> New Equation

{−x + y = 3

________

`\displaystyle 1(2)/(3) ≠ 0; NO\:SOLUTION`

_______________________________________________

12) {−3x - 8y = 20

{−5x + y = 19

⅛[−3x - 8y = 20]

{−⅜x - y = 2½ >> New Equation

{−5x + y = 19

__________

`\displaystyle (-5(3)/(8)x)/(-5(3)/(8)) = (21(1)/(2))/(-5(3)/(8))`

`\displaystyle x = -4`[Plug this back into both equations above to get the y-coordinate of −1];
`\displaystyle -1 = y`

_______________________________________________

11) {x + 3y = 1

{−3x - 3y = −15

___________

`\displaystyle (-2x)/(-2) = (-14)/(-2)`

`\displaystyle x = 7`[Plug this back into both equations above to get the y-coordinate of −2];
`\displaystyle -2 = y`

I am delighted to assist you anytime my friend!