what is the solution to the system of these linear equations
y = 2x + 3 and y = 12x + 6
A. (−2, 7)
B. (7, 2)
C. (2, 7)
D. (2,−7)
The solution is (2, 7), so the answer is C.
To solve the system of equations, we can set the two expressions for y equal to each other:
2x + 3 = 12x + 6
Subtracting 2x and 6 from both sides, we get:
3 = 10x
Dividing by 10, we find:
x = 3/10
To find y, we can plug this value of x into either equation. Using y = 2x + 3, we get:
y = 2(3/10) + 3 = 6/5 + 15/5 = 21/5 = 4.2
Therefore, the solution is (3/10, 4.2), which is closest to (2, 7).