How do you solve for a in ax+ z = aw-yax+z=awy?

1 Answer
Apr 12, 2018

See a solution process below:

Explanation:

First, subtract color(red)(z)z and color(blue)(aw)aw from each side of the equation to isolate the aa terms while keeping the equation balanced:

ax - color(blue)(aw) + z - color(red)(z) = aw - color(blue)(aw) - y - color(red)(z)axaw+zz=awawyz

ax - aw + 0 = 0 - y - zaxaw+0=0yz

ax - aw = -y - zaxaw=yz

Next, factor an aa from each term on the left side of the equation:

a(x - w) = -y - za(xw)=yz

Now, divide each side of the equation by color(red)(x - w)xw to solve for aa while keeping the equation balanced:

(a(x - w))/color(red)(x - w) = (-y - z)/color(red)(x - w)a(xw)xw=yzxw

(acolor(red)(cancel(color(black)((x - w)))))/cancel(color(red)(x - w)) = (-y - z)/(x - w)

a = (-y - z)/(x - w)

We can then multiply the right side of the equation by a form of 1 to rewrite the expression as:

a = (-1)/-1 xx (-y - z)/(x - w)

a = (-1(-y - z))/(-1(x - w))

a = (y + z)/(-x + w)

a = (y + z)/(w - x)