How do you determine whether a linear system has one solution, many solutions, or no solution when given 8x =+ y = -16 and -3x + y = - 5?

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Answer 1 · 2018-04-10T20:42:43

There is one solution. #x=-1# and #y=-8#

I'm assuming the two equations are

Equation I: #8x+y=-16#, and

Equation II: #-3x+y=-5#.

I will subtract Equation II from Equation I.

#8x+y-(-3x)-y=-16-(-5)#

Which simplifies to

#11x=-11#.

Divide both sides by 11.

#x=-1#

Substitute #x=-1# into Equation II.

#-3(-1)+y=-5#.

Simplify.

#3+y=-5#

Subtract three from both sides of this equation.

#y=-8#

There is one solution. #x=-1# and #y=-8#