To quickly determine the number of solutions of a linear system of equations, we need to express each of the equations in slope-intercept form, so we can compare their slopes, and decide:

1) if they intersect at a unique point (when the slopes are different) thus giving a one solution, or

2) if the slopes have the exact same value giving parallel lines (with no intersections, and the y-intercept is different so there is no solution), or

3) if there is an infinite number of solutions (both lines are exactly the same, that is same slope and same y-intercept)

So we write them in slope -intercept form:

First equation:

$6x+y=-1\\y=-6x-1$

second equation:

$-6x-4y=4\\-6x=4y+4\\-6x-4=4y\\y=-\frac{3}{2} x-1$

So we see that their slopes are different (for the first one slope = -6, and for the second one slope= -3/2) and then the lines must intercept in a one unique point. Therefore the system of equations has a one unique solution.

6 0

2 years ago

Express as a ratio in whole numbers 1/2 : 1/4 : 1/12

Gelneren [198K]

Answer:

6 : 3 : 1

Step-by-step explanation:

Given

$\frac{1}{2}$ : $\frac{1}{4}$ : $\frac{1}{12}$ ( multiply each part by 12 , the LCM of 2, 3, 12 to clear the fractions )