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
<pre>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(matrix(1,5, y, "=", (- 9)/5, or, - 1.8))}}}
3x - 7(- 1.8) = 6 ------ Substituting - 1.8 for y in eq (i)
3x + 12.6 = 6
3x = - 6.6
{{{highlight_green(matrix(1,5, x, "=", (- 6.6)/3, "=", - 2.2))}}}