To solve the system of equations using substitution, we start with the equations:
- 3x + 2y = 7
- y = 3x + 11
We can substitute the expression for y from the second equation into the first equation. This gives us:
3x + 2(3x + 11) = 7
Next, we distribute the 2:
3x + 6x + 22 = 7
Simplifying this, we combine like terms:
9x + 22 = 7
Now, we isolate x by subtracting 22 from both sides:
9x = 7 – 22
9x = -15
Now, we divide by 9 to solve for x:
x = -/9 or x = -5/3
Now that we have x, we can substitute this back into the second equation to find y:
y = 3(-5/3) + 11
y = -5 + 11
y = 6
Thus, the solution set of the system is:
(x, y) = (-5/3, 6)
In conclusion, the solution set of the system of equations 3x + 2y = 7 and y = 3x + 11 is the point (-5/3, 6).