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Use the elimination method to solve each system. If there is no solution, or infinitely many solutions, so state.
$$\left\{\begin{array}{l}{3 x-5 y=-29} \\{3 x-5 y=15}\end{array}\right.$$
No solution
Algebra
Chapter 4
Systems of Linear Equations and Inequalities
Section 3
Solving Systems of Equations by Elimination (Addition)
Equations and Inequalities
Systems of Equations and Inequalities
Campbell University
Harvey Mudd College
Baylor University
Idaho State University
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to use the elimination method we need to have opposite ex coefficients or opposite why coefficients and we don't have that yet, But we can multiply one of the equations by negative one. And so how about if I multiply the first equation by negative one that will make it negative. Three. X Plus five Why equals 29? And I'll leave the second equation alone. So it's still three x minus five y equals 15. So now when we add the equations together we have opposite coefficients on X, so the exes are eliminated. We also have opposite coefficients on Why so the wise air eliminated so everything on the left is eliminated, leaving us with zero equals on the other side, we add, and we get 44. Zero equals 44 is a contradiction of false statement. It's not true. That is our clue that this system actually has no solutions. These would be two parallel lines
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