Question 1 $$ \left.\begin{array}{l} ext { Use elimination to solve the system of equations. } \ -2 x+3 y=48 \ 7 x+3 y=21 \ ( \end{array} ight) $$

Question

Question 1 $$ \left.\begin{array}{l}	ext { Use elimination to solve the system of equations. } \ -2 x+3 y=48 \ 7 x+3 y=21 \ ( \end{array}ight) $$

UpStudy AI · Accepted Answer

1. Write down the system of equations:
   $$
   \begin{cases}
   -2x + 3y = 48, \
   7x + 3y = 21.
   \end{cases}
   $$

2. Eliminate $$ y $$ by subtracting the first equation from the second:
   $$
   (7x + 3y) - (-2x + 3y) = 21 - 48.
   $$

3. Simplify the left-hand side:
   $$
   7x + 3y + 2x - 3y = 9x.
   $$

4. Simplify the right-hand side:
   $$
   21 - 48 = -27.
   $$
   Hence,
   $$
   9x = -27.
   $$

5. Solve for $$ x $$ by dividing both sides by 9:
   $$
   x = \frac{-27}{9} = -3.
   $$

6. Substitute $$ x = -3 $$ into one of the original equations (using the second equation):
   $$
   7(-3) + 3y = 21.
   $$

7. Simplify:
   $$
   -21 + 3y = 21.
   $$

8. Add 21 to both sides:
   $$
   3y = 42.
   $$

9. Solve for $$ y $$:
   $$
   y = \frac{42}{3} = 14.
   $$

10. The solution to the system is:
    $$
    x = -3, \quad y = 14.
    $$
The solution to the system is $$ x = -3 $$ and $$ y = 14 $$.

Question 1