Solve the system of equations(If the system is dependent, enter a general solution in terms of c):
in Other Math Topics by

Your answer

Your name to display (optional):
Privacy: Your email address will only be used for sending these notifications.
Anti-spam verification:
To avoid this verification in future, please log in or register.

1 Answer

Call the three equations A, B and C. Note that if we double C we get the same constant 6 as B. So we can write B=2C. That is, 70x+12y+4z=29x+5y+3z. So 41x+7y+z=0. Similarly, note that A=-C. That is, 6x+y-z=-35x-6y-2z. So 41x+7y+z=0. And B=-2A: 29x+5y+3z=-12x-2y+2z, or 41x+7y+z=0. So, because we've involved all three equations and discovered a common equation, there's dependence between the three equations and therefore no unique solution, but we can take one of the assumed variables and consider it as we would a constant. Let's call that constant c. The three equations can now be rewritten 6x+y=c-3, 29x+5y=6-3c, 35x+6y=3-2c. We only need two of these to find x and y. Take the first two and multiply the first by 5 and subtract the second: 30x+5y=5c-15 subtract 29x+5y=6-3c and we get x=8c-21. Substitute this in the first equation and we get 6(8c-21)+y=c-3, from which y=123-47c. We can check the answer by putting in c=0, for example, and checking out the three original equations after substituting for x and y.

by Top Rated User (1.1m points)

Related questions

Welcome to MathHomeworkAnswers.org, where students, teachers and math enthusiasts can ask and answer any math question. Get help and answers to any math problem including algebra, trigonometry, geometry, calculus, trigonometry, fractions, solving expression, simplifying expressions and more. Get answers to math questions. Help is always 100% free!

Most popular tags

algebra problems solving equations word problems calculating percentages math problem geometry problems calculus problems math fraction problems trigonometry problems rounding numbers simplifying expressions solve for x order of operations probability algebra pre algebra problems word problem evaluate the expression slope intercept form statistics problems factoring polynomials solving inequalities 6th grade math how to find y intercept equation of a line sequences and series algebra 2 problems logarithmic equations solving systems of equations by substitution dividing fractions greatest common factor square roots geometric shapes graphing linear equations long division solving systems of equations least to greatest dividing decimals substitution method proving trigonometric identities least common multiple factoring polynomials ratio and proportion trig identity precalculus problems standard form of an equation solving equations with fractions http: mathhomeworkanswers.org ask# function of x calculus slope of a line through 2 points algebraic expressions solving equations with variables on both sides college algebra domain of a function solving systems of equations by elimination differential equation algebra word problems distributive property solving quadratic equations perimeter of a rectangle trinomial factoring factors of a number fraction word problems slope of a line limit of a function greater than or less than geometry division fractions how to find x intercept differentiation exponents 8th grade math simplifying fractions geometry 10th grade equivalent fractions inverse function area of a triangle elimination method story problems standard deviation integral ratios simplify systems of equations containing three variables width of a rectangle percentages area of a circle circumference of a circle place value solving triangles parallel lines mathematical proofs solving linear equations 5th grade math mixed numbers to improper fractions scientific notation problems quadratic functions number of sides of a polygon length of a rectangle statistics zeros of a function prime factorization percents algebra 1 evaluating functions derivative of a function equation area of a rectangle lowest common denominator solving systems of equations by graphing integers algebra 2 diameter of a circle dividing polynomials vertex of a parabola calculus problem perpendicular lines combining like terms complex numbers geometry word problems converting fractions to decimals finding the nth term range of a function 4th grade math greatest to least ordered pairs functions radius of a circle least common denominator slope unit conversion solve for y calculators solving radical equations calculate distance between two points area word problems equation of a tangent line multiplying fractions chemistry binomial expansion place values absolute value round to the nearest tenth common denominator sets set builder notation please help me to answer this step by step significant figures simplifying radicals arithmetic sequences median age problem trigonometry graphing derivatives number patterns adding fractions radicals midpoint of a line roots of polynomials product of two consecutive numbers limits decimals compound interest please help pre-algebra problems divisibility rules graphing functions subtracting fractions angles numbers discrete mathematics volume of a cylinder simultaneous equations integration probability of an event comparing decimals factor by grouping vectors percentage expanded forms rational irrational numbers improper fractions to mixed numbers algebra1 matrices logarithms how to complete the square mean statistics problem analytic geometry geometry problem rounding decimals 5th grade math problems solving equations with variables solving quadratic equations by completing the square simplifying trigonometric equation using identities
87,441 questions
99,039 answers
2,422 comments
16,939 users