Mathematics
For solving each pair of equations, use the method of elimination by equating coefficients :
3 - (x - 5) = y + 2
2(x + y) = 4 - 3y
Linear Equations
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Answer
Simplifying first equation :
⇒ 3 - (x - 5) = y + 2
⇒ 3 - x + 5 = y + 2
⇒ 8 - x = y + 2
⇒ x + y + 2 - 8 = 0
⇒ x + y - 6 = 0 …….(1)
Simplifying second equation :
⇒ 2(x + y) = 4 - 3y
⇒ 2x + 2y = 4 - 3y
⇒ 2x + 2y + 3y = 4
⇒ 2x + 5y - 4 = 0 ……(2)
Multiplying equation (1) by 2, we get :
⇒ 2(x + y - 6) = 2 × 0
⇒ 2x + 2y - 12 = 0 …….(3)
Subtracting equation (3) from (2), we get :
⇒ 2x + 5y - 4 - (2x + 2y - 12) = 0
⇒ 2x - 2x + 5y - 2y - 4 + 12 = 0
⇒ 3y + 8 = 0
⇒ 3y = -8
⇒ y = .
Substituting value of y in equation (1), we get :
Hence, x = .
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