Let x represent one number and let y represent the other number. Use the given conditions to write a system of equations. Solve the system and find the numbers. Write a system of equations. A. $$ \begin{cases} 5x + y = -29 \\ x + y = -10 \end{cases} $$ C. $$ \begin{cases} x - 5y = -10 \\ x - y = -28 \end{cases} $$ B. $$ \begin{cases} 2x - y = -11 \\ x + 4y = -28 \end{cases} $$ D. $$ \begin{cases} 2x - y = -11 \\ x + y = -28 \end{cases} $$
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Step 2: Translate the first condition into an equation. "Twice a first number decreased by a second number is -11." "Twice a first number" means 2x. "decreased by a second number" means -y. So, the first equation is: $$2x - y = -11$$ Step 3: Translate the second Show more…
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Rachel L.
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Consider the following system of equations: 2x - y = 12 -3x - 5y = -5 The steps for solving the given system of equations are shown below: Step one: -5(2x - y = 12) -3x - 5y = -5 Step two: -10x + 5y = -5 Step three: -13x = -65 Step four: x = 5 Step five: 2(5) - y = 12 Step six: y = -2 Solution: (5, -2) Select the correct statement about step three. A. When the equations -10x + 5y = -60 and -3x - 5y = -5 are added together, a third linear equation, -13x = -65, is formed, and it has a different solution from the original equations. B. When the equation -3x - 5y = -5 is subtracted from -10x + 5y = -60, a third linear equation, -13x = -65, is formed, and it has a different solution from the original equations. C. When the equations -10x + 5y = -60 and -3x - 5y = -5 are added together, a third linear equation, -13x = -65, is formed, and it shares a common solution with the original equations. D. When the equation -3x - 5y = -5 is subtracted from -10x + 5y = -60, a third linear equation, -13x = -65, is formed, and it shares a common solution with the original equations.
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