Solve by substitution: -2x+1=2y, 7x-4y-13=0
First, we can solve for y in the first equation* by dividing both sides by 2:
-2x+1=2y
y=(-2x+1)/2
We can now substitute this y term into the second equation and solve for x:
7x-4y-13=0
7x-4((-2x+1)/2)=13
Notice that we can cancel a 2 from the numerator and denominator:
7x-2(-2x+1)=13
7x+4x-2=13
Combining x-terms and moving all constants to one side, we find the value of x:
11x=15
x=15/11
To solve for y, we plug in the x value we just found into the first equation which we solved for y and solve for the y value which corresponds with x=15/11:
y=(-2x+1)/2
=(-2(15/11)+1)/2
=((-30)/11+1)/2
=((-30+11)/11)/2
=-19/22
Therefore, the solution to the linear system of equations is (15/11,-19/22)
*This was chosen because we can see that if we solve for y in the first equation and plug into the second equation, the 1/2 resulting from dividing the first equation by 2 would cancel out with the 4 in the second equation when we substitute in (since 2 is a factor of 4). Solving for any other variable and substituting into the other equation would result in some unwanted fraction which would thus complicate the problem a bit more than necessary.