How can we solve the system of equations 2y = 5 and 2x + 4y = 10?

To solve the system of equations given by:

• 1. 2y = 5
• 2. 2x + 4y = 10

We can start by solving the first equation for y:

1. From 2y = 5, divide both sides by 2:
2. y = 5 / 2
3. y = 2.5

Now that we have the value of y, we can substitute y = 2.5 into the second equation to solve for x:

1. Substituting into the second equation:
2. 2x + 4(2.5) = 10
3. 2x + 10 = 10

Next, we will isolate x:

1. Subtract 10 from both sides:
2. 2x = 10 – 10
3. 2x = 0

Finally, divide both sides by 2:

1. x = 0

In conclusion, the solution to the system of equations is:

• x = 0
• y = 2.5

This means the point of intersection of the two equations is (0, 2.5).