Describe in words how we could have solved the following by

Describe in words how we could have solved the following by elimination: {1/3 x + 1/2 y = 7 2/3 x - y = -2 Explain when you might use substitution rather than the elimination. Consider the system of equations y = 4x + 3 and y = 2x + 5 a. Use the symmetric and transitive properties of equality to write a statement about 4x + 3 and 2x - 5. b. Explain how you could solve the system of equations now. c. If you graph the system of equations, where would the lines intersect? You Decide when Helen solves the system of equations 4y - 8x = 28 and y = 2x - 5, the result is -20 = 28. Helen decides that the graphs of the equations are the same line. Juanita says that the graphs of the lines. Who is correct, and why? Describe the three different possibilities that may occur when graphing a system of two linear equations. What types of solutions occur with each possibility?

Solution

x/3 + y/2 = 7

2x/3 - y = -2

By elemination : multiply equation 1 by 2 to make the coeffecient of varible y same in both

equations same , so that it can be eleminated

2x/3 +y = 14

Now add the two equation:

2x/3 +y = 14

2x/3 - y = -2

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4x/3 = 12 ; x= 9

y = 14 -2x/3 = 14 - 2*9/3 = 14 - 6 = 8

(x, y) = ( 9 , 8) This is the solution