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{:[7x+10 y=60],[7x-2y=240]:} If (x,y) satisfies the given system of equations, what is the value of x ?

7x+10yamp;=607x−2yamp;=240 \begin{aligned} 7 x+10 y & =60 \\ 7 x-2 y & =240 \end{aligned} \newlineIf (x,y) (x, y) satisfies the given system of equations, what is the value of x x ?

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Q. 7x+10y=607x−2y=240 \begin{aligned} 7 x+10 y & =60 \\ 7 x-2 y & =240 \end{aligned} \newlineIf (x,y) (x, y) satisfies the given system of equations, what is the value of x x ?
  1. Elimination Method: Let's solve the system of equations using the elimination method. We will subtract the second equation from the first to eliminate xx and find the value of yy.\newlineCalculation: (7x+10y)−(7x−2y)=60−240(7x + 10y) - (7x - 2y) = 60 - 240\newlineSimplifying, we get: 10y+2y=60−24010y + 2y = 60 - 240\newline12y=−18012y = -180\newlineDivide both sides by 1212 to find yy: y=−18012y = -\frac{180}{12}\newliney=−15y = -15
  2. Calculate y: Now that we have the value of yy, we can substitute it back into one of the original equations to find xx. Let's use the first equation 7x+10y=607x + 10y = 60.\newlineCalculation: 7x+10(−15)=607x + 10(-15) = 60\newline7x−150=607x - 150 = 60\newlineAdd 150150 to both sides: 7x=60+1507x = 60 + 150\newline7x=2107x = 210\newlineDivide both sides by 77 to find xx: x=2107x = \frac{210}{7}\newlinex=30x = 30

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