Solve the system using substitution.
y = 4x − 5
y = 2x + 1
A. (−2, −3)
B. (1, 3)
C. (−2, −13)
D. (3, 7)
Sub the second equation into the first.
2x+1=4x-5
2x=6
x=3
y=2x+1
7=2(3)+1
7=7
The answer would be D.
To solve the system using substitution, we need to solve one of the equations for one variable, and then substitute that expression into the other equation. Let's solve the second equation for y in terms of x:
y = 2x + 1
Now, we can substitute this expression for y in the first equation:
4x - 5 = 2x + 1
Next, we can isolate x by moving all terms with x to one side of the equation:
4x - 2x = 1 + 5
2x = 6
Dividing both sides of the equation by 2 gives us:
x = 3
Now that we have found the value of x, we can substitute it back into either equation to solve for y. Let's use the second equation:
y = 2(3) + 1
y = 6 + 1
y = 7
Therefore, the solution to the system is (x, y) = (3, 7).
So, the correct answer choice is D. (3, 7).