Question

In the following system of equations, determine whether the system has a unique

infinitely many solutions or no solution.
2x +3y =7,
6x + 5y =
11
​

Answer 1

the system has a unique solution

Explanation:

Start with an equation of a line in standard form,

`ax + by = c`

Solve it for y to put it into the slope-intercept form:

`by = -ax + c`

`y = -(a)/(b)x + (c)/(b)`

The slope is -a/b.

Now look at your system of equations. The slope of the first equation is -a/b = -2/3. The slope of the second equation is -a/b = -6/5.

You have a system of two linear equations with two lines with different slopes, so the lines must intersect at a single point.

Answer: the system has a unique solution