Question

solve the system by the addition method.

( x + 2y = 4 )
( -2x + 3y = 13 )

Explanation:

Step1: Eliminate x by multiplying first equation

Multiply the first equation \(x + 2y = 4\) by 2, we get \(2x + 4y = 8\).

Step2: Add the two equations

Add the new equation \(2x + 4y = 8\) to the second equation \(-2x + 3y = 13\). So, \((2x - 2x)+(4y + 3y)=8 + 13\), which simplifies to \(7y = 21\).

Step3: Solve for y

Divide both sides of \(7y = 21\) by 7, we get \(y=\frac{21}{7}=3\).

Step4: Substitute y into first equation

Substitute \(y = 3\) into \(x + 2y = 4\), we have \(x+2\times3 = 4\), so \(x + 6 = 4\).

Step5: Solve for x

Subtract 6 from both sides: \(x=4 - 6=-2\).

Answer:

The solution of the system is \(x = - 2\), \(y = 3\) (or the ordered pair \((-2,3)\))