Question

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question 1(multiple choice worth 5 points)
(solve systems of equations by elimination mc)
what is the solution to the given system of equations?
4x + 5y = 6
x - y = -3
○ (-5, -2)
○ (-4, -1)
○ (-3, 0)
○ (-1, 2)

Explanation:

Step1: Multiply the second equation

To eliminate \(x\) or \(y\), we can multiply the second equation \(x - y=-3\) by \(4\) to make the coefficient of \(x\) equal to \(4\) (same as in the first equation). So we get \(4(x - y)=4\times(-3)\), which simplifies to \(4x-4y = - 12\).

Step2: Subtract the new equation from the first

Now we have the first equation \(4x + 5y=6\) and the new equation \(4x-4y=-12\). Subtract the second from the first: \((4x + 5y)-(4x - 4y)=6-(-12)\). Simplifying the left side: \(4x+5y - 4x + 4y=9y\), and the right side: \(6 + 12 = 18\). So \(9y=18\), dividing both sides by \(9\) gives \(y = 2\).

Step3: Substitute \(y\) into the second equation

Substitute \(y = 2\) into \(x - y=-3\), we get \(x-2=-3\). Adding \(2\) to both sides, \(x=-3 + 2=-1\).

Answer:

\((-1,2)\) (corresponding to the option with \((-1,2)\))