How do you solve the system of equations #5x + y = 11# and #- 3x - 7y = - 13#?

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Answer 1 · 2017-03-24T23:12:53

#x = 2#

#y = 1#

Solving by addition/ elimination
The plan is to eliminate either one of the variables; #y# seems easier.

Eqn 1: #" "5x + y = 11#

Eqn 2: #" " -3x -7y = -13#

Multiply eqn 1 by #7# to make it eqn 3:

#35x + 7y = 77#

Add eqn 3 + eqn 2:

#32x = 64#

Dividing both sides by #32#, we get

#x = 2#

Substitute #x = 2# into any of the equations, let's say eqn 1 in this case

#5 * (2) + y = 11#

#10 + y =11#

#y = 1#