53) \\( \\left\\{ \\begin{array} { l } { x - 2 y = - 6 } \\\\ { - 7 x - 6 y = 22 } \\end{array} \\right. \\)
53) \\( \\left\\{ \\begin{array} { l } { x - 2 y = - 6 } \\\\ { - 7 x - 6 y = 22 } \\end{array} \\right. \\)
Answer
Explanation:
Step1: Express (x) in terms of (y) from the first equation
From (x - 2y=-6), we get (x = 2y - 6).
Step2: Substitute (x = 2y - 6) into the second equation
Substitute into (-7x-6y = 22), we have (-7(2y - 6)-6y=22). Expand the left - hand side: (-14y + 42-6y=22). Combine like terms: (-20y+42 = 22). Subtract 42 from both sides: (-20y=22 - 42=-20). Divide both sides by (-20): (y = 1).
Step3: Find the value of (x)
Substitute (y = 1) into (x = 2y - 6), we get (x=2\times1 - 6=-4).
Answer:
(x=-4,y = 1)