How do solve the following linear system?: # -x+5y=-5 , -7x+y=-19 #?

1 Answer
May 10, 2016

Answer:

#x = 45/17# and #y = -8/17#

Explanation:

There are several methods to solve simultaneous equations:

Substitution, elimination, or by equating two variables.

Let's make y the subject in both equations:

Equ 1: #5y = x - 5" Equ 2": y = 7x - 19#
#" " y = x/5 - 1#

The two y values are equal: y = y
Therefore: # x/5 - 1 = 7x - 19 " " xx 5#

# x - 5 = 35x - 95 " solve for "x#
#90 = 34x#
#90/34 = x rArr " "x = 45/17#

Now that we have the value for x, substitute into both equations to check the value for y.

# y = 45/17 ÷ 5 - 1# and # y = 7 (45/17) - 19#
# y = -8/17 " "y = -8/17#