Use elimination to solve the system of equations.

Ask by Ortiz Willis. in the United States

Mar 24,2025

Question

Use elimination to solve the system of equations. $$ -2 x+3 y=48 $$ $$ 7 x+3 y=21 $$

UpStudy AI · Accepted Answer

1. Write the given system of equations:
   $$
   -2x + 3y = 48
   $$
   $$
   7x + 3y = 21
   $$

2. Since both equations have the term $$3y$$, we can eliminate $$y$$ by subtracting the first equation from the second:
   $$
   (7x + 3y) - (-2x + 3y) = 21 - 48
   $$

3. Simplify the left side by distributing the subtraction:
   $$
   7x + 3y + 2x - 3y = 9x
   $$
   The right side simplifies to:
   $$
   21 - 48 = -27
   $$

4. Now, we have the equation:
   $$
   9x = -27
   $$

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 first equation):
   $$
   -2(-3) + 3y = 48
   $$
   Simplify:
   $$
   6 + 3y = 48
   $$

7. Isolate $$y$$ by subtracting 6 from both sides:
   $$
   3y = 42
   $$

8. Divide both sides by 3:
   $$
   y = 14
   $$

Thus, the solution to the system is:
$$
x = -3 \quad \text{and} \quad y = 14
$$
The solution is $$ x = -3 $$ and $$ y = 14 $$.

Use elimination to solve the system of equations.

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