Thread: Algebra - Linear systems

1.
a) For what value of a is there no unique solution for the following simultaneous equations.
3x - 2y = 5
5x + ay = 4

b) When a has this value is there an infinite number of solutions or no solution? Justify your answer.

2.
Solve for x: 3 - x/4 < 2 - 3x/5

Originally Posted by LilDragonfly

1.
a) For what value of a is there no unique solution for the following simultaneous equations.
3x - 2y = 5
5x + ay = 4

b) When a has this value is there an infinite number of solutions or no solution? Justify your answer.

2.
Solve for x: 3 - x/4 < 2 - 3x/5

1.
That happens when the determinant is zero, thus,

Thus,

Thus,
.

To determine if this system is consistent or inconsistent substitute the value of yields,


Note:I multiplied to second equation by 3 to clear denominator.

Now, multiply the first equation by 5 to yield,


How can ?
Impossible, thus this system is inconsistent.

2.
You have,

Multiply by LCD=20,

Add 5x to both sides,

Subtract 40 from both sides,

Divide both sides by -7 remember to flip sign ,