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?

1 Answer
Apr 10, 2018

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

Explanation:

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