Question

Giving 40 points

Solve each system by substitution

Answer 1

Explanation:

`\underline{ \underline{ \text{Given}}} :`

• -4x - y = 19 -------- Equation ( i )
• x - 2y = -7 ----------- Equation ( ii )

`\underline{ \underline{ \text{To \: find}}} :`

• Value of x & y

`\underline {\underline{ \text{ Solution}}} :`

From equation ( i ) :

-4x - y = 19

-y = 19 + 4x

-y = - ( -19 - 4x )

y = -4x - 19 ------ Equation ( iii )

Substituting the value of y from equation ( iii ) in equation ( ii ) , we get :

`\tt{x - 2y = - 7 }`

⇾
`\tt{x - 2( - 4x - 19) = - 7}`

⇾
`\tt{x + 8x + 38 = - 7}`

⇾
`\tt{9x = - 7 - 38}`

⇾
`\tt{9x = - 45}`

⇾
`\tt{x = ( - 45)/(9)}`

⇾
`\boxed{ \tt{x = - 5}}`

Substituting the value of x in equation ( i ) , we get :

⇾
`\tt{ - 5 - 2y = - 7}`

⇾
`\tt{ - 2y = - 7 + 5}`

⇾
`\tt{ - 2y = - 2}`

⇾
`\tt{y = ( - 2)/( - 2)}`

⇾
`\boxed{ \tt{y = 1}}`

The possible solution of the system is ordered pair ( x , y ) = ( -5 , 1 ) .

`\red{ \boxed{ \boxed { \tt{Our \: final \: answer : \boxed{ \tt{( - 5 \:, 1 \: )}}}}}}`

Hope I helped ! ツ

Have a wonderful day / night ! ♡

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