Question

-10x-3y=-18
-7x-8y=11 solve system using elimination
​

Answer 1

`\huge{ \boxed{ \text{(3 \:, - 4)}}}`

✑
`\underline{ \underline{ \text{First ,\: let's \: know \: about \: elimination \: method}}}` :

☇ In this method , we add or subtract the given equations to eliminate one of the two variables by making their coefficients equal. Then , a single equation with one variable so obtained is solved to find the value of the variable. The value of the variable is substituted to any one equation to find the value of the eliminated variable.

☯
`\underline{ \underline{ \text{Let's \: solve}}} :`

`\underline{ \text{Original \: system}} :`

`\text{ - 10x - 3y = - 18 - - - - Equation\: (i)}`

`\text{ - 7x - 8y = 11 - - - - Equation \: (ii)}`

`\text{Step \: 1} :` Take L.C.M ( Lowest Common Multiple ) of 10 and 7. For this , find the prime factors of each number. Then, take out the common prime factors and other remaining prime factors and multiply them.

• prime factors of 10 = 1 × 2 × 5
• prime factors of 7 = 1 × 7

L.C.M = Common factors × Remaining Factors

= 1 × 2 × 5 × 7

= 70

`\text{Step \: 2} :` Multiply equation ( i ) by 7

`\text{7( - 10x - 3y ) = - 18  * 7}`

⇢
`\text{ - 70x - 21y = - 126 - - - - equation \: (iii)}`

`\text{Step \: 3} :`Multiply equation ( ii ) by 10

`\text{10( - 7x - 8y) = 11 \: * \: 10}`

⇢
`\text{ - 70x - 80y = 110 - - - - equation \: (iv)}`

`\text{Step \: 4} :` Subtract equation ( iv ) from equation ( iii ) :

Also Remember that while subtracting , sign of each term of the second equation changes. Here , we are eliminating x . So to make the coefficient of y same , equation ( i ) is multiplied by 7 and equation ( ii ) is multiplied by 10.⇩

`\text{ - 70x - 21y = - 126}`

`\text{+70x + 80y = - 110}`

___________________

`\text{ \: \: \: \: \: \: 59y = - 236}`

Solve :

⇢
`\text{59y/59 = - 236/59}`

⇢
`\boxed{ \bold{ \text{y = - 4}}}`

`\text{Step \: 5} :`

Substitute the value of y into equation ( iii ) , we get :

`\text{ - 70x - 21y = - 126}`

➳
`\text{ - 70x - 21( - 4) = - 126}`

➳
`\text{ - 70x - ( - 84) = - 126}`

➳
`\text{ - 70x + 84 = - 126}`

➳
`\text{ - 70x = - 126 - 84}`

➳
`\text{ - 70x = - 210}`

➳
`\text{ - 70x/  - 70 = - 210/  - 70}`

➳
`\boxed{ \bold{ \text{x = 3}}}`

`\bold{ \underline{ \text{Hence ,\: x = 3 \: and \: y = - 4}}}`

Hope I helped!

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`\sf{TheAnimeGirl}` ♪

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Answer 2

(-7) (-10x - 3y = -18)

(10) (-7x - 8x = 11)

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70x + 21y = 126

+ -70 - 80x = 110

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-59x = 236

x = -4