To solve the system of equations, we have:
- Equation 1: y = 2x + 3
- Equation 2: x + 2y = 14
We can start by substituting the expression for y from Equation 1 into Equation 2. This way, we replace y in Equation 2 with 2x + 3:
Substituting into Equation 2:
x + 2(2x + 3) = 14
Now, expand and simplify:
x + 4x + 6 = 14
5x + 6 = 14
Next, isolate x:
5x = 14 – 6
5x = 8
x = 8/5
x = 1.6
Now that we have the value of x, we can substitute it back into Equation 1 to find y:
y = 2(1.6) + 3
y = 3.2 + 3
y = 6.2
Therefore, the solution to the system of equations is:
(x, y) = (1.6, 6.2)
This means that the two lines represented by these equations intersect at the point (1.6, 6.2).