Discover answers to your most pressing questions at Westonci.ca, the ultimate Q&A platform that connects you with expert solutions. Join our platform to connect with experts ready to provide detailed answers to your questions in various areas. Discover in-depth answers to your questions from a wide network of professionals on our user-friendly Q&A platform.
Sagot :
Sure, let's solve the system of equations step-by-step.
We start with the given system of equations:
1. [tex]\(\frac{x-1}{2} = y - 1\)[/tex]
2. [tex]\(2x = \frac{y}{2} + 5\)[/tex]
Step 1: Simplify the first equation
[tex]\(\frac{x-1}{2} = y - 1\)[/tex]
Multiply both sides by 2 to clear the fraction:
[tex]\[ x - 1 = 2(y - 1) \][/tex]
[tex]\[ x - 1 = 2y - 2 \][/tex]
Rearrange to solve for [tex]\(x\)[/tex]:
[tex]\[ x = 2y - 1 + 1 \][/tex]
[tex]\[ x = 2y - 1 + 2 \][/tex]
[tex]\[ x = 2y - 1 \][/tex]
Step 2: Simplify the second equation
[tex]\(2x = \frac{y}{2} + 5\)[/tex]
Multiply both sides by 2 to clear the fraction:
[tex]\[ 4x = y + 10 \][/tex]
Rearrange to solve for [tex]\(y\)[/tex]:
[tex]\[ y = 4x - 10 \][/tex]
Step 3: Substitute [tex]\(y = 4x - 10\)[/tex] into the first equation
We already have [tex]\( x = 2y - 1\)[/tex]:
[tex]\[ x = 2(4x - 10) - 1 \][/tex]
[tex]\[ x = 8x - 20 - 1 \][/tex]
[tex]\[ x = 8x - 21 \][/tex]
Now, solve for [tex]\(x\)[/tex]:
[tex]\[ x - 8x = -21 \][/tex]
[tex]\[ -7x = -21 \][/tex]
[tex]\[ x = 3 \][/tex]
Step 4: Substitute [tex]\(x = 3\)[/tex] back into [tex]\(y = 4x - 10\)[/tex]
[tex]\[ y = 4(3) - 10 \][/tex]
[tex]\[ y = 12 - 10 \][/tex]
[tex]\[ y = 2 \][/tex]
Thus, the solution to the system of equations is:
[tex]\[ (x, y) = (3, 2) \][/tex]
We start with the given system of equations:
1. [tex]\(\frac{x-1}{2} = y - 1\)[/tex]
2. [tex]\(2x = \frac{y}{2} + 5\)[/tex]
Step 1: Simplify the first equation
[tex]\(\frac{x-1}{2} = y - 1\)[/tex]
Multiply both sides by 2 to clear the fraction:
[tex]\[ x - 1 = 2(y - 1) \][/tex]
[tex]\[ x - 1 = 2y - 2 \][/tex]
Rearrange to solve for [tex]\(x\)[/tex]:
[tex]\[ x = 2y - 1 + 1 \][/tex]
[tex]\[ x = 2y - 1 + 2 \][/tex]
[tex]\[ x = 2y - 1 \][/tex]
Step 2: Simplify the second equation
[tex]\(2x = \frac{y}{2} + 5\)[/tex]
Multiply both sides by 2 to clear the fraction:
[tex]\[ 4x = y + 10 \][/tex]
Rearrange to solve for [tex]\(y\)[/tex]:
[tex]\[ y = 4x - 10 \][/tex]
Step 3: Substitute [tex]\(y = 4x - 10\)[/tex] into the first equation
We already have [tex]\( x = 2y - 1\)[/tex]:
[tex]\[ x = 2(4x - 10) - 1 \][/tex]
[tex]\[ x = 8x - 20 - 1 \][/tex]
[tex]\[ x = 8x - 21 \][/tex]
Now, solve for [tex]\(x\)[/tex]:
[tex]\[ x - 8x = -21 \][/tex]
[tex]\[ -7x = -21 \][/tex]
[tex]\[ x = 3 \][/tex]
Step 4: Substitute [tex]\(x = 3\)[/tex] back into [tex]\(y = 4x - 10\)[/tex]
[tex]\[ y = 4(3) - 10 \][/tex]
[tex]\[ y = 12 - 10 \][/tex]
[tex]\[ y = 2 \][/tex]
Thus, the solution to the system of equations is:
[tex]\[ (x, y) = (3, 2) \][/tex]
Thanks for using our platform. We aim to provide accurate and up-to-date answers to all your queries. Come back soon. We hope you found this helpful. Feel free to come back anytime for more accurate answers and updated information. We're here to help at Westonci.ca. Keep visiting for the best answers to your questions.