To find the solution set of the system of equations 3x + 2y = 7 and y = 3x + 11, we can use the substitution method.
First, let’s start with the second equation:
y = 3x + 11
This equation expresses y in terms of x, making it convenient to substitute this expression for y in the first equation.
Next, substitute y in the first equation:
3x + 2(3x + 11) = 7
Now, distribute 2 in the equation:
3x + 6x + 22 = 7
Combine like terms:
9x + 22 = 7
Now, isolate x by subtracting 22 from both sides:
9x = 7 – 22
9x = -15
Next, divide both sides by 9:
x = - rac{15}{9} = - rac{5}{3}
Having found the value of x, we can now find y using the second equation:
y = 3(- rac{5}{3}) + 11
Calculating this gives:
y = -5 + 11 = 6
Thus, we have x = - rac{5}{3} and y = 6. The solution set of the system of equations is:
(x, y) = (- rac{5}{3}, 6)
In conclusion, the solution set of the given system of equations is:
{(-5/3, 6)}