How do solve the following linear system?: # -2x+3y=-1 , -x-7y=14 #?
First, solve equation #2 for x.
This gives you
Now substitute this value of x into the 1st equation, like this:
Multiply the negative 2 into the parentheses:
Combine like terms:
Move the 28 to the other side of the equation:
Divide both sides by 17 to isolate the y-term:
which gives you:
Since 17 and 29 are both prime numbers, the answer cannot be reduced.
Now you have the value of y. Plug that into the either eqn:
and solve for x.
Divide both sides by negative 2:
The fractions look odd, but it checks out.