Question

solve the system by the addition method.
4x + 6y = 10
2x + 7y = 17

Explanation:

Step1: Eliminate x by multiplying the second equation

Multiply the second equation \(2x + 7y = 17\) by \(-2\) to get \(-4x - 14y = -34\).

Step2: Add the two equations

Add the first equation \(4x + 6y = 10\) and the new second equation \(-4x - 14y = -34\):
\((4x - 4x)+(6y - 14y)=10 - 34\)
\(-8y = -24\)

Step3: Solve for y

Divide both sides by \(-8\): \(y=\frac{-24}{-8}=3\)

Step4: Substitute y into an original equation

Substitute \(y = 3\) into \(2x + 7y = 17\):
\(2x+7(3)=17\)
\(2x + 21 = 17\)
Subtract 21 from both sides: \(2x=17 - 21=-4\)
Divide by 2: \(x=\frac{-4}{2}=-2\)

Answer:

The solution is \(x = -2\), \(y = 3\) or \((-2, 3)\)