Question Find the solution of the system of equations. $$ -3 x-7 y=18 $$ $$ 9 x+2 y=3 $$ $$ \begin{array}{l}\text { Answer Attempt tout of a } \ (\square), \square) \text { Submit Answer }\end{array} $$

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UpStudy AI · Accepted Answer

1. Write down the system of equations:
   $$
   -3x - 7y = 18
   $$
   $$
   9x + 2y = 3
   $$

2. Multiply the first equation by $$3$$ to match the coefficient of $$x$$ (in absolute value):
   $$
   3(-3x - 7y) = 3(18) \quad \Rightarrow \quad -9x - 21y = 54
   $$

3. Now, add the modified first equation and the second equation to eliminate $$x$$:
   $$
   \begin{aligned}
   (-9x - 21y) + (9x + 2y) &= 54 + 3 \
   (-9x + 9x) + (-21y + 2y) &= 57 \
   -19y &= 57
   \end{aligned}
   $$

4. Solve for $$y$$:
   $$
   y = \frac{57}{-19} = -3
   $$

5. Substitute $$y = -3$$ back into one of the original equations to solve for $$x$$. Using the first equation:
   $$
   -3x - 7(-3) = 18 \quad \Rightarrow \quad -3x + 21 = 18
   $$
   $$
   -3x = 18 - 21 \quad \Rightarrow \quad -3x = -3
   $$
   $$
   x = \frac{-3}{-3} = 1
   $$

6. The solution to the system is:
   $$
   (x, y) = (1, -3)
   $$
The solution to the system of equations is $$ (1, -3) $$.

Question Find the solution of the system of equations. \[ -3 x-7 y=18 \] \[ 9 x+2 y=3 \] \( \begin{array}{l}\text { Answer Attempt tout of a } \\ (\square), \square) \text { Submit Answer }\end{array} \)

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