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Simplifying 10y + -10z + -45 = 12y + 21z + -51 Reorder the terms: -45 + 10y + -10z = 12y + 21z + -51 Reorder the terms: -45 + 10y + -10z = -51 + 12y + 21z Solving -45 + 10y + -10z = -51 + 12y + 21z Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Add '-12y' to each side of the equation. -45 + 10y + -12y + -10z = -51 + 12y + -12y + 21z Combine like terms: 10y + -12y = -2y -45 + -2y + -10z = -51 + 12y + -12y + 21z Combine like terms: 12y + -12y = 0 -45 + -2y + -10z = -51 + 0 + 21z -45 + -2y + -10z = -51 + 21z Add '45' to each side of the equation. -45 + -2y + 45 + -10z = -51 + 45 + 21z Reorder the terms: -45 + 45 + -2y + -10z = -51 + 45 + 21z Combine like terms: -45 + 45 = 0 0 + -2y + -10z = -51 + 45 + 21z -2y + -10z = -51 + 45 + 21z Combine like terms: -51 + 45 = -6 -2y + -10z = -6 + 21z Add '10z' to each side of the equation. -2y + -10z + 10z = -6 + 21z + 10z Combine like terms: -10z + 10z = 0 -2y + 0 = -6 + 21z + 10z -2y = -6 + 21z + 10z Combine like terms: 21z + 10z = 31z -2y = -6 + 31z Divide each side by '-2'. y = 3 + -15.5z Simplifying y = 3 + -15.5z
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