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

To solve the system of equations, we have:

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

First, let’s solve Equation 2 for one of the variables. We can express y in terms of x:

y = 10 - x

Now that we have y expressed in terms of x, we can substitute this into Equation 1:

3x + 2(10 - x) = 5

This simplifies to:

3x + 20 - 2x = 5

Now, combine like terms:

x + 20 = 5

Next, isolate x by subtracting 20 from both sides:

x = 5 - 20

x = -15

Now that we have the value of x, we can plug it back into the equation we derived for y:

y = 10 - (-15)

This gives us:

y = 10 + 15

y = 25

So, the solution to the system of equations is:

• x = -15
• y = 25

In conclusion, the values of x and y that solve the given system of equations are -15 and 25, respectively.