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Simplifying m(ax + by) + n(ex + dy) = mc + nf (ax * m + by * m) + n(ex + dy) = mc + nf (amx + bmy) + n(ex + dy) = mc + nf Reorder the terms: amx + bmy + n(dy + ex) = mc + nf amx + bmy + (dy * n + ex * n) = mc + nf amx + bmy + (dny + enx) = mc + nf Solving amx + bmy + dny + enx = cm + fn Solving for variable 'a'. Move all terms containing a to the left, all other terms to the right. Add '-1bmy' to each side of the equation. amx + bmy + dny + -1bmy + enx = cm + -1bmy + fn Reorder the terms: amx + bmy + -1bmy + dny + enx = cm + -1bmy + fn Combine like terms: bmy + -1bmy = 0 amx + 0 + dny + enx = cm + -1bmy + fn amx + dny + enx = cm + -1bmy + fn Reorder the terms: amx + dny + enx = -1bmy + cm + fn Add '-1dny' to each side of the equation. amx + dny + -1dny + enx = -1bmy + cm + -1dny + fn Combine like terms: dny + -1dny = 0 amx + 0 + enx = -1bmy + cm + -1dny + fn amx + enx = -1bmy + cm + -1dny + fn Add '-1enx' to each side of the equation. amx + enx + -1enx = -1bmy + cm + -1dny + -1enx + fn Combine like terms: enx + -1enx = 0 amx + 0 = -1bmy + cm + -1dny + -1enx + fn amx = -1bmy + cm + -1dny + -1enx + fn Divide each side by 'mx'. a = -1bx-1y + cx-1 + -1dm-1nx-1y + -1em-1n + fm-1nx-1 Simplifying a = -1bx-1y + cx-1 + -1dm-1nx-1y + -1em-1n + fm-1nx-1
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