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Chapter 14: Chapter 14

Problem 324

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Solve \(x+y=3\) \(2 x+3 y=1\)

Short Answer

Expert verified
The solution to the system of equations is \(x=8\) and \(y=-5\).
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TABLE OF CONTENTS :
TABLE OF CONTENTS

Step 1: Solve one equation for one variable

We will start by solving the first equation for y: \(x+y=3\) Subtract x from both sides of the equation to isolate y: \(y=3-x\)

Step 2: Substitute the expression for y into the other equation

Now we will substitute the expression \(3-x\) for y in the second equation: \(2x + 3y = 1\) Replace y with its expression: \(2x + 3(3-x) = 1\)

Step 3: Solve for x

Now, we need to solve this equation for x. First, distribute the 3 to the terms inside the parentheses: \(2x + 9 - 3x = 1\) Now, combine like terms: \(2x - 3x + 9 = 1\) Solve for x: \(-x = -8\) \(x = 8\)

Step 4: Find the value of y

Now that we have the value of x, we can find the value of y by substituting the value of x into the expression we found for y in step 1: \(y = 3 - x\) \(y = 3 - 8\) \(y = -5\)

Step 5: Write the solution

Our solution is: \(x = 8\) and \(y = -5\) So, the system of equations is solved by the values \(x=8\) and \(y=-5\).

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