QQuestionMathematics
QuestionMathematics
"Question content area top
Part 1
Solve the system by the substitution method.
left brace Start 2 By 1 Matrix 1st Row 1st Column 4 x plus 5 y equals negative 13 2nd Row 1st Column x equals y minus 1 EndMatrix
Question content area bottom
Part 1
Select the correct choice below and, if necessary, fill in the answer box to complete your choice.
A. There is exactly one solution. The solution set is StartSet nothing EndSet.
(Simplify your answer. Type an ordered pair.)
B. There are infinitely many solutions. The solution set is StartSet left parenthesis x comma y right parenthesis | 4 x plus 5 y equals negative 13 EndSet or StartSet left parenthesis x comma y right parenthesis |x equals y minus 1 EndSet.
C. The solution set is empty set."
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Answer
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Step 1:: First, we will solve the second equation for $y$:
y = x + 1 \quad \text{(By substitution method, solve for y in the second equation)}
Step 2:: Next, substitute the expression for $y$ from Step 1 into the first equation:
4x + 5(x + 1) = -13
Step 3:: Simplify the equation from Step 2:
9x + 5 = -13
Step 4:: Subtract 5 from both sides of the equation from Step 3:
9x = -18
Step 5:: Divide both sides of the equation from Step 4 by 9:
x = \frac{-18}{9} = -2
Step 6:: Substitute the value of $x$ from Step 5 into the equation for $y$ from Step 1:
y = (-2) + 1 = -1
Step 7:: Since both $x$ and $y$ have been found, the system has a unique solution.
Final Answer
The answer corresponds to choice A.
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