Question

Consider the following system of equations: `4x + 3y = 3color(white)("ddd")` `2x - 3y = -5` What can be said about the system of equations? No Solution Two Solutions One Solution Infinitely Many Solutions

Answer 1

1 solution. That is where they cross they both share the same points

Explanation:

These are equations of strait lines.

Converting them into the standardised form of `y=mx+c` gives:

`y=-4/3x+1" ".......... Equation(1)`

`y=2/3x+5/3" "............Equation(2)`

`Eqn(1)` slopes downward reading left to right
as `4/3x` is negative `->-4/3x`

`Eqn(2)` slopes up reading left to right
as `2/3x` is positive.

As one is NOT superimposed on the other then there is NOT an infinite count of solutions.

The graphs well 'cross' at some point as they have different gradients (slopes). So there is 1 solution.