What is the solution set of the following system of equations 5x + 3y = 10 and x + y = 7?

To find the solution set of the system of equations, we need to solve them simultaneously. The two equations we are given are:

• Equation 1: 5x + 3y = 10
• Equation 2: x + y = 7

We can start by solving the simpler Equation 2 for one of the variables. Let’s express y in terms of x:

y = 7 - x

Now, we can substitute this expression for y back into Equation 1:

5x + 3(7 - x) = 10

Next, distribute the 3:

5x + 21 - 3x = 10

Combine like terms:

2x + 21 = 10

Now, isolate x by subtracting 21 from both sides:

2x = 10 - 21

2x = -11

Now, divide both sides by 2:

x = -rac{11}{2}

With the value of x found, we can substitute it back into the expression for y:

y = 7 - (-rac{11}{2})

This simplifies to:

y = 7 + rac{11}{2} = rac{14}{2} + rac{11}{2} = rac{25}{2}

Thus, the solution set for the system of equations is:

(x, y) = igg(-rac{11}{2}, rac{25}{2}igg)

In conclusion, the solution set for the system of equations is {(-11/2, 25/2)}.