How do you solve this system of equations: #2a - b = 17 and 3a + 4b = - 13#?

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Answer 1 · 2017-11-28T02:15:47

See a solution process below:

Step 1) Solve the first equation for #b#;

#2a - b + color(red)(b) - color(blue)(17) = 17 - color(blue)(17) + color(red)(b)#

#2a - 0 - color(blue)(17) = 0 + color(red)(b)#

#2a - 17 = b#

#b = 2a - 17#

Step 2) Substitute #(2a - 17)# for #b# in the second equation and solve for #a#:

#3a + 4b = -13# becomes:

#3a + 4(2a - 17) = -13#

#3a + (4 xx 2a) - (4 xx 17) = -13#

#3a + 8a - 68 = -13#

#(3 + 8)a - 68 = -13#

#11a - 68 = -13#

#11a - 68 + color(red)(68) = -13 + color(red)(68)#

#11a - 0 = 55#

#11a = 55#

#(11a)/color(red)(11) = 55/color(red)(11)#

#(color(red)(cancel(color(black)(11)))a)/cancel(color(red)(11)) = 5#

#a = 5#

Step 3) Substitute #5# for #a# in the solution to the first equation at the end of Step 1 and calculate #b#:

#b = 2a - 17# becomes:

#b = (2 xx 5) - 17#

#b = 10 - 17#

#b = -7#

The Solution Is: #a = 5# and #b = -7#