Question

Please help solve by elimination I hope its not blurry Have a nice day and Goodnight

Answer 1

`\displaystyle \textcolor{black}{4.}\:[-3, -5]`

`\displaystyle \textcolor{black}{3.}\:[8, -1]`

`\displaystyle \textcolor{black}{2.}\:[4, -7]`

`\displaystyle \textcolor{black}{1.}\:[3, -2]`

Explanation:

When using the Elimination method, you eradicate one pair of variables so they are set to zero. It does not matter which pair is selected:

`\displaystyle \left \{ {{2x - 3y = 9} \atop {-5x - 3y = 30}} \right.`

{2x - 3y = 9

{⅖[−5x - 3y = 30]

`\displaystyle \left \{ {{2x - 3y = 9} \atop {-2x - 1(1)/(5)y = 12}} \right. \\ \\ (-4(1)/(5)y)/(-4(1)/(5)) = (21)/(-4(1)/(5)) \\ \\ \boxed{y = -5, x = -3}`

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`\displaystyle \left \{ {{x - 2y = 10} \atop {x + 3y = 5}} \right.`

{x - 2y = 10

{⅔[x + 3y = 5]

`\displaystyle \left \{ {{x - 2y = 10} \atop {(2)/(3)x + 2y = 3(1)/(3)}} \right. \\ \\ (1(2)/(3)x)/(1(2)/(3)) = (13(1)/(3))/(1(2)/(3)) \\ \\ \boxed{x = 8, y = -1}`

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`\displaystyle \left \{ {{y = -3x + 5} \atop {y = -8x + 25}} \right.`

{y = −3x + 5

{−⅜[y = −8x + 25]

`\displaystyle \left \{ {{y = -3x + 5} \atop {-(3)/(8)y = 3x - 9(3)/(8)}} \right. \\ \\ ((5)/(8)y)/((5)/(8)) = (-4(3)/(8))/((5)/(8)) \\ \\ \boxed{y = -7, x = 4}`

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`\displaystyle \left \{ {{y = -x + 1} \atop {y = 4x - 14}} \right.`

{y = −x + 1

{¼[y = 4x - 14]

`\displaystyle \left \{ {{y = -x + 1} \atop {(1)/(4)y = x - 3(1)/(2)}} \right. \\ \\ (1(1)/(4)y)/(1(1)/(4)) = (-2(1)/(2))/(1(1)/(4)) \\ \\ \boxed{y = -2, x = 3}`

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I am joyous to assist you at any time.