To solve the equations h = 5x + 3 and j = 2x, we need to find the values of h and j in terms of x first. Then we’ll look to find the total h + j and check if it equals 2.
Let’s break it down step-by-step:
- Substituting for j: From the second equation,
j = 2x - Finding h + j: Now, substituting j into the equation for h + j:
h + j = (5x + 3) + (2x) - Simplifying: Combine like terms:
h + j = 5x + 2x + 3 = 7x + 3 - Setting up the equation: We want to find out when h + j = 2:
7x + 3 = 2 - Solving for x:
7x = 2 – 3
7x = -1
x = -1/7
Now that we have x, we can find the corresponding value of h and j:
- Finding j:
j = 2x = 2(-1/7) = -2/7 - Finding h:
h = 5x + 3 = 5(-1/7) + 3 = -5/7 + 3 = -5/7 + 21/7 = 16/7
Lastly, let’s verify by adding them:
h + j = (16/7) + (-2/7) = 16/7 – 2/7 = 14/7 = 2
Thus, we find that h + j does equal 2 when x = -1/7.
Now, considering the options provided: 1723, 17, and 23 are mentioned, but none directly relate to the value calculated from h + j = 2.