Which pair of equations share a solution?
Answer: 5x+2=32
4x+9=5(14-x)-7
-I know the answer but I have absolutely no idea how to get it help please!
solve for x in each equation. Are they both the same?
yes! thank you very much
To find the solution to a pair of equations, you need to solve each equation separately and see if there is a value for x that makes both equations true.
Let's solve each equation step by step:
Equation 1: 5x + 2 = 32
Step 1: Subtract 2 from both sides of the equation:
5x = 32 - 2
5x = 30
Step 2: Divide both sides of the equation by 5 to solve for x:
x = 30/5
x = 6
Now, let's move on to the second equation:
Equation 2: 4x + 9 = 5(14 - x) - 7
Step 1: Simplify the right side of the equation:
4x + 9 = 70 - 5x - 7
Step 2: Combine like terms on the right side of the equation:
4x + 9 = -5x + 63
Step 3: Add 5x to both sides of the equation:
4x + 5x + 9 = 63
Step 4: Combine like terms on the left side of the equation:
9x + 9 = 63
Step 5: Subtract 9 from both sides of the equation:
9x = 63 - 9
9x = 54
Step 6: Divide both sides of the equation by 9 to solve for x:
x = 54/9
x = 6
Now that we have solved both equations, we can compare the solutions. In this case, both equations have the same solution, which is x = 6. Therefore, the pair of equations share a solution.
So, the answer is:
5x + 2 = 32
4x + 9 = 5(14 - x) - 7
I hope this explanation helps! Let me know if you have any further questions.