Question

16 -5x - 5y = -25 + 7x + 2y = 30

Explanation:

Step1: Eliminate a variable (y)

First, we can multiply the first equation by 2 and the second equation by 5 to make the coefficients of y opposite.
For the first equation \(-5x - 5y = -25\), multiply by 2: \(2\times(-5x - 5y)=2\times(-25)\) gives \(-10x - 10y = -50\)
For the second equation \(7x + 2y = 30\), multiply by 5: \(5\times(7x + 2y)=5\times30\) gives \(35x + 10y = 150\)

Step2: Add the two new equations

Now add the two equations \(-10x - 10y = -50\) and \(35x + 10y = 150\) together.
\((-10x + 35x)+(-10y + 10y)=-50 + 150\)
Simplify: \(25x=100\)

Step3: Solve for x

Divide both sides of \(25x = 100\) by 25: \(x=\frac{100}{25}=4\)

Step4: Substitute x into one of the original equations

Let's use the second original equation \(7x + 2y = 30\). Substitute \(x = 4\) into it:
\(7\times4+2y=30\)
\(28 + 2y=30\)

Step5: Solve for y

Subtract 28 from both sides: \(2y=30 - 28 = 2\)
Divide both sides by 2: \(y = 1\)

Answer:

\(x = 4\), \(y = 1\)