To solve the system of equations given by:
1. 2x + y = 7
2. y = 2x + 3
We can use the substitution method. Since the second equation already expresses y in terms of x, we can substitute this expression into the first equation.
Substituting y from the second equation into the first equation, we get:
2x + (2x + 3) = 7
Now, let’s combine like terms:
2x + 2x + 3 = 7
4x + 3 = 7
Next, we isolate x:
4x = 7 – 3
4x = 4
x = 1
Now that we have the value of x, we can find y by substituting x = 1 back into the second equation:
y = 2(1) + 3
y = 2 + 3
y = 5
Thus, the solution to the system of equations is:
(x, y) = (1, 5)
In conclusion, the solution to the equations 2x + y = 7 and y = 2x + 3 is the point (1, 5).