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Find the solution of the system of equations
-3x-2y=-4
9x+3y=15

User Dancer
by
8.7k points

2 Answers

3 votes

Final answer:

The solution to the system of equations -3x-2y=-4 and 9x+3y=15 is found by using the elimination method, resulting in x = 2 and y = -1.

Step-by-step explanation:

The solution to the system of equations given by:

  • -3x - 2y = -4
  • 9x + 3y = 15

can be found using several methods, such as substitution or elimination. In this situation, the elimination method might be the simplest since the coefficients of x in both equations are multiples of each other. The steps are as follows:

  1. Multiply the first equation by 3 to make the coefficients of x in both equations the same in magnitude but opposite in sign.
  2. Add the modified first equation to the second equation to eliminate x.
  3. Solve the resulting single-variable equation for y.
  4. Substitute the value of y back into one of the original equations to solve for x.

Following these steps:

  1. Multiply the first equation by 3:
  • (-3x - 2y) * 3 = -4 * 3
  • -9x - 6y = -12
Add the modified first equation to the second:
  • -9x - 6y + 9x + 3y = -12 + 15
  • -3y = 3
Divide by -3 to solve for y:
  • y = -1
Substitute y = -1 into the second original equation:
  • 9x + 3(-1) = 15
  • 9x - 3 = 15
  • Add 3 to both sides:
  • 9x = 18
  • Divide by 9:
  • x = 2

The solution to the system of equations is x = 2 and y = -1.

User Ullsokk
by
8.3k points
6 votes

Answer: x = 2, y = -1

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User AlefSin
by
8.3k points

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