Question

Solve {3x+2y=15x−3y=8 by elimination. Express your answer as an ordered pair.

Answer 1

As given by the question

There are given that the system of equation:

$\begin{gathered} 3x+2y=1\ldots(1) \\ 5x-3y=8\ldots(2) \end{gathered}$

Now,

Multiply by 5 with the equation (1) and multiply by 3 with the equation (2)

Then,

$\begin{gathered} (3x+2y=1)\times5=15x+10y=5\ldots(3) \\ (5x-3y=8)\times3=15x-9y=24\ldots(4) \end{gathered}$

Now,

Subtract equation (4) from equation (3)

So,

$\begin{gathered} 10y-(-9y)=5-24 \\ 10y+9y=5-24 \\ 19y=-19 \\ y=-1 \end{gathered}$

Then,

Put the value of y into the equation (1)

So,

$\begin{gathered} 3x+2y=1 \\ 3x+2(-1)=1 \\ 3x-2=1 \\ 3x=1+2 \\ 3x=3 \\ x=1 \end{gathered}$

Hence, the answer as an ordered pair is (1, -1).