Answer:To solve the system of equations: 2x + y + 5z = 6 (Equation 1) 5x - y - 7z = 1 (Equation 2) x - y - 3z = -3 (Equation 3) We can use the method of elimination or substitution. Let's use the method of elimination. 1. Multiply Equation 1 by 5 and Equation 2 by 2 to eliminate the y term: 10x + 5y + 25z = 30 (Equation 4) 10x - 2y - 14z = 2 (Equation 5) 2. Subtract Equation 5 from Equation 4 to eliminate the x term: (10x + 5y + 25z) - (10x - 2y - 14z) = 30 - 2 7y + 39z = 28 (Equation 6) 3. Multiply Equation 2 by 3 and Equation 3 by 5 to eliminate the y term: 15x - 3y - 21z = 3 (Equation 7) 5x - 5y - 15z = -15 (Equation 8) 4. Add Equation 7 to Equation 8 to eliminate the x term: (15x - 3y - 21z) + (5x - 5y - 15z) = 3 - 15 20x - 8y - 36z = -12 (Equation 9) 5. Multiply Equation 6 by 4 and Equation 9 by 7 to eliminate the y term: 28y + 156z = 112 (Equation 10) 140x - 56y - 252z = -84 (Equation 11) 6. Add Equation 10 to Equation 11 to eliminate the x term: (28y + 156z) + (140x - 56y - 252z) = 112 - 84 140x + 28y - 96z = 28 (Equation 12) 7. Divide Equation 12 by 28 to simplify: 5x + y - 3z = 1 (Equation 13) 8. Now we have two equations with two variables: 7y + 39z = 28 (Equation 6) 5x + y - 3z = 1 (Equation 13) We can solve this system of equations using any method, such as substitution or elimination. I hope this explanation helps! Let me know if you have any further questions.
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