Question

d. 5(-10x + 3y = 1) 10(-5x - 6y = 23)

Explanation:

Step1: Multiply first equation by 5

Multiply each term in \(-10x + 3y = 1\) by 5.
\(5\times(-10x)+5\times(3y)=5\times1\)
\(-50x + 15y = 5\)

Step2: Multiply second equation by 10

Multiply each term in \(-5x - 6y = 23\) by 10.
\(10\times(-5x)+10\times(-6y)=10\times23\)
\(-50x - 60y = 230\)

(Assuming the goal is to eliminate \(x\) by subtracting or adding the equations. If we subtract the second new equation from the first: \((-50x + 15y)-(-50x - 60y)=5 - 230\))

Step3: Simplify the subtraction

\(-50x + 15y + 50x + 60y=-225\)
\(75y=-225\)

Step4: Solve for \(y\)

Divide both sides by 75: \(y=\frac{-225}{75}=-3\)

Step5: Substitute \(y = - 3\) into one of the original equations (e.g., first original equation \(-10x+3y = 1\))

\(-10x+3\times(-3)=1\)
\(-10x - 9 = 1\)

Step6: Solve for \(x\)

Add 9 to both sides: \(-10x=1 + 9=10\)
Divide by - 10: \(x=\frac{10}{-10}=-1\)

Answer:

The solution to the system of equations is \(x=-1\), \(y = - 3\)