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

To solve the system of equations algebraically, we start by writing down the equations:

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

Next, we can eliminate one of the variables by subtracting one equation from the other. Let’s subtract Equation 2 from Equation 1:

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

This simplifies to:

2x = 4

Now, we can solve for x by dividing both sides by 2:

x = 2

Now that we have the value of x, we can substitute it back into one of the original equations to solve for y. Let’s use Equation 1:

5(2) + 2y = 10

This simplifies to:

10 + 2y = 10

Subtracting 10 from both sides, we get:

2y = 0

Dividing both sides by 2 gives us:

y = 0

So, the solution to the system of equations is (x, y) = (2, 0).

To verify, we can substitute these values back into both original equations:

• For Equation 1: 5(2) + 2(0) = 10 which holds true.
• For Equation 2: 3(2) + 2(0) = 6 which also holds true.

This confirms that our solution is correct.