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Simplifying 5r(a + -1b) + s(a + -1b) = 0 (a * 5r + -1b * 5r) + s(a + -1b) = 0 (5ar + -5br) + s(a + -1b) = 0 5ar + -5br + (a * s + -1b * s) = 0 5ar + -5br + (as + -1bs) = 0 Reorder the terms: 5ar + as + -5br + -1bs = 0 Solving 5ar + as + -5br + -1bs = 0 Solving for variable 'a'. Move all terms containing a to the left, all other terms to the right. Add '5br' to each side of the equation. 5ar + as + -5br + 5br + -1bs = 0 + 5br Combine like terms: -5br + 5br = 0 5ar + as + 0 + -1bs = 0 + 5br 5ar + as + -1bs = 0 + 5br Remove the zero: 5ar + as + -1bs = 5br Add 'bs' to each side of the equation. 5ar + as + -1bs + bs = 5br + bs Combine like terms: -1bs + bs = 0 5ar + as + 0 = 5br + bs 5ar + as = 5br + bs Reorder the terms: 5ar + as + -5br + -1bs = 5br + -5br + bs + -1bs Combine like terms: 5br + -5br = 0 5ar + as + -5br + -1bs = 0 + bs + -1bs 5ar + as + -5br + -1bs = bs + -1bs Combine like terms: bs + -1bs = 0 5ar + as + -5br + -1bs = 0 The solution to this equation could not be determined.
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