How can I solve the system of equations 3x + 4y = 9 and 3x + 2y = 9 using the elimination method?

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To solve the system of equations using elimination, we start by stating the equations clearly:

  • Equation 1: 3x + 4y = 9
  • Equation 2: 3x + 2y = 9

The goal of the elimination method is to eliminate one of the variables, allowing us to solve for the other. In this case, we can eliminate the variable x.

First, we notice that both equations have the same coefficient for x (which is 3). We can use this property to eliminate x by subtracting one equation from the other.

Let’s subtract Equation 2 from Equation 1:

   (3x + 4y) - (3x + 2y) = 9 - 9

When we perform this subtraction, we get:

   3x + 4y - 3x - 2y = 0

This simplifies to:

   4y - 2y = 0

Which further simplifies to:

   2y = 0

Now, we can solve for y:

   y = 0

With y now known, we can substitute y = 0 back into either of the original equations to solve for x. Let’s use Equation 1:

   3x + 4(0) = 9

This simplifies to:

   3x = 9

Now, solve for x: 

   x = 9 / 3 = 3

So, the solution to the system of equations is:

  • x = 3
  • y = 0

In conclusion, the solution can be expressed as the coordinate point (3, 0). This means that the lines represented by both equations intersect at this point on the Cartesian plane.

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