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Simplifying y[4] = 0.7y[4 + -1] + 0.3u[4 + -1] Reorder the terms for easier multiplication: 4y = 0.7y[4 + -1] + 0.3u[4 + -1] Combine like terms: 4 + -1 = 3 4y = 0.7y[3] + 0.3u[4 + -1] Reorder the terms for easier multiplication: 4y = 0.7 * 3y + 0.3u[4 + -1] Multiply 0.7 * 3 4y = 2.1y + 0.3u[4 + -1] Combine like terms: 4 + -1 = 3 4y = 2.1y + 0.3u[3] Reorder the terms for easier multiplication: 4y = 2.1y + 0.3 * 3u Multiply 0.3 * 3 4y = 2.1y + 0.9u Reorder the terms: 4y = 0.9u + 2.1y Solving 4y = 0.9u + 2.1y Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Add '-2.1y' to each side of the equation. 4y + -2.1y = 0.9u + 2.1y + -2.1y Combine like terms: 4y + -2.1y = 1.9y 1.9y = 0.9u + 2.1y + -2.1y Combine like terms: 2.1y + -2.1y = 0.0 1.9y = 0.9u + 0.0 1.9y = 0.9u Divide each side by '1.9'. y = 0.4736842105u Simplifying y = 0.4736842105u
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