Question

.Solve the pair of linear equations 3x + 15y -13 =0 and
2x-5y -7=0 and hence find the value of m forwhich=
y= mx - 3​

Answer 1

7x + 5y - 3z = 16 (equation 1)

3x - 5y + 2z = -8 (equation 2)

5x + 3y - 7z = 0 (equation 3)

14x + 10y - 6z = 32 (equation 1 multiplied by 2)

9x - 15y + 6z = -24 (equation 2 multiplied by 3)

23x - 5y = 8 (equation 4, from adding the 2 equations above)

21x - 35y + 14z = - 56 (equation 2 multiplied by 7)

10x + 6y - 14z = 0 (equation 3 multiplied by 2)

31x - 29y = -56 (equation 5, from adding the 2 equations above)

667x - 145y = 232 (equation 4 multiplied by 29)

155x - 145y = -280 (equation 5 multiplied by 5)

512x = 512 (equation 4 multiplied by 29 - equation 5 multiplied by 5)

x = 1 (equation 6)

Substitute equation 6 into equation 4

23(1) - 5y = 8

-5y = -15

y = 3 (equation 7)

Substitute equation 6 and equation 7 into equation 1

7(1) + 5(3) - 3z = 16

22 - 3z = 16

-3z = -6

z = 2 (equation 8)

(x, y, z) = (1, 3, 2)