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{:[-4x-2y=16],[4x+3y=-18]:}

−4x−2y=164x+3y=−18 \begin{array}{l}-4 x-2 y=16 \\ 4 x+3 y=-18\end{array}

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Full solution

Q. −4x−2y=164x+3y=−18 \begin{array}{l}-4 x-2 y=16 \\ 4 x+3 y=-18\end{array}
  1. Write Equations: First, let's write down the system of equations: {−4x−2y=16 4x+3y=−18\begin{cases} -4x-2y=16 \ 4x+3y=-18 \end{cases}
  2. Use Elimination Method: We can use the method of elimination to solve this system. Let's add the two equations together to eliminate xx.(−4x−2y)+(4x+3y)=16−18(-4x - 2y) + (4x + 3y) = 16 - 18
  3. Solve for y: Now, let's do the math:\newline−4x+4x−2y+3y=−2-4x + 4x - 2y + 3y = -2\newline0x+y=−20x + y = -2\newliney=−2y = -2
  4. Substitute yy into Equation: We found the value of yy, now let's substitute y=−2y = -2 into one of the original equations to find xx. We'll use the first equation:\newline−4x−2(−2)=16-4x - 2(-2) = 16
  5. Solve for x: Simplify the equation: −4x+4=16-4x + 4 = 16
  6. Solve for x: Simplify the equation:\newline−4x+4=16-4x + 4 = 16Now, let's solve for x:\newline−4x=16−4-4x = 16 - 4\newline−4x=12-4x = 12\newlinex=12−4x = \frac{12}{-4}\newlinex=−3x = -3

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