SOLUTION: Solve this set of linear equations using the substitution method. Be sure to show all your work. 3x – 7y = 6 2x – 3y = 1

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Question 1131307: Solve this set of linear equations using the substitution method. Be sure to show all your work.

3x – 7y = 6
2x – 3y = 1
Found 2 solutions by MathLover1, MathTherapy:
Answer by MathLover1(20850) About Me  (Show Source):
You can put this solution on YOUR website!

Solved by pluggable solver: SOLVE linear system by SUBSTITUTION
Solve:
+system%28+%0D%0A++++3%5Cx+%2B+-7%5Cy+=+6%2C%0D%0A++++2%5Cx+%2B+-3%5Cy+=+1+%29%0D%0A++We'll use substitution. After moving -7*y to the right, we get:
3%2Ax+=+6+-+-7%2Ay, or x+=+6%2F3+-+-7%2Ay%2F3. Substitute that
into another equation:
2%2A%286%2F3+-+-7%2Ay%2F3%29+%2B+-3%5Cy+=+1 and simplify: So, we know that y=-1.8. Since x+=+6%2F3+-+-7%2Ay%2F3, x=-2.2.

Answer: system%28+x=-2.2%2C+y=-1.8+%29.

Answer by MathTherapy(10552) About Me  (Show Source):
You can put this solution on YOUR website!

Solve this set of linear equations using the substitution method. Be sure to show all your work.

3x – 7y = 6
2x – 3y = 1
3x – 7y = 6 ------- eq (i)

2x – 3y  = 1 ------ eq (ii)

In order to avoid fractions, do the following:

1)  Multiply the 1st equation by 2, and solve for 6x to get: 6x - 14y = 12_____6x = 12 + 14y ------ eq (iii)

2)  Multiply the 2nd equation by 3 to get: 6x - 9y = 3 ------ eq (iv)

3)  Substitute 12 + 14y for 6x in eq (iv) to get: 12 + 14y - 9y = 3

5y = - 9

highlight_green%28matrix%281%2C5%2C+y%2C+%22=%22%2C+%28-+9%29%2F5%2C+or%2C+-+1.8%29%29

3x - 7(- 1.8) = 6 ------ Substituting - 1.8 for y in eq (i)

3x + 12.6 = 6

3x = - 6.6