How can I solve the system of equations 5x + 2y = 10 and 3x + 2y = 6 algebraically?

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Solving the System of Equations Algebraically

To solve the system of equations:

  • Equation 1: 5x + 2y = 10
  • Equation 2: 3x + 2y = 6

We will use the elimination method to find the values of x and y.

Step 1: Align the Equations

We start with both equations: 

5x + 2y = 10  
3x + 2y = 6

Step 2: Eliminate One Variable

Since both equations have 2y terms, we can eliminate y by subtracting Equation 2 from Equation 1:

(5x + 2y) - (3x + 2y) = 10 - 6

This simplifies to:

2x = 4

Step 3: Solve for x

Now, divide both sides by 2:

x = 2

Step 4: Substitute x back into one of the original equations

We can substitute x = 2 back into Equation 1 to solve for y:

5(2) + 2y = 10  
10 + 2y = 10  
2y = 0

Now, divide both sides by 2:

y = 0

Step 5: Write the Solution

The solution to the system of equations is:

  • x: 2
  • y: 0

In conclusion, the values of x and y that solve the system of equations 5x + 2y = 10 and 3x + 2y = 6 are:

(x, y) = (2, 0)

Feel free to substitute these values back into the original equations to verify that they satisfy both equations!

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