How many solution does this have and how do you solve it
1 answer:
Answer:
Infinite solutions
Step-by-step explanation:
To determine the number of solutions a system has, you need its slope. If the slopes are the same, check if the equations are equivalent or not.
To find the slope, rearrange the equation to isolate "y", which makes it slope-intercept form y = mx + b.
"x" and "y" represent points on the line.
"m" represents the slope, which is how steep a line is.
"b" represents the y-intercept (where the graph hits the y-axis).
Isolate "y" in both equations:
x + 3y = 0
3y = -x Subtract 'x' from both sides
y = -x/3 Divide both sides by 3.
y =
The slope is -1/3.
9y = -3x
y = -3x/9 Divide both sides by 9
y = Reduce the fraction to lowest terms
y =
The slope is -1/3, but the two equations are the same.
Since the equations are the same, or <u>equivalent</u>, the two lines are always touching. The solution of a system means where two lines intersect, or meet. Therefore, <u>there are infinite solutions</u>.
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Answer:
Option 3 - 4 miles
Step-by-step explanation:
Given : In a city, the distance between the library and the police station is 3 miles less than twice the distance between the police station and the fire station. The distance between the library and the police station is 5 miles.
To find : How far apart are the police station and the fire station?
Solution :
Let the distance between police station and fire station be 'x'.
The distance between the library and the police station is 3 miles less than twice the distance between the police station and the fire station.
i.e.
The distance between the library and the police station is 5 miles.
i.e.
Therefore, The police and fire stations is 4 miles apart.
So, Option 3 is correct.
Answer:
Option A = 7.5 cups
Step-by-step explanation:
Given : Suppose you're making a soup that uses 5 cups of chicken broth and teaspoons of corn starch for 8 servings. You need to make 12 servings of the soup, so you'll need
teaspoons of corn starch.
To find : How much broth do you need?
Solution :
A soup that uses 5 cups of chicken broth and teaspoons of corn starch for 8 servings.
i.e. 5 cups + teaspoon = 8 servings ......(1)
You need to make 12 servings of the soup, so you'll need
i.e. x cups + teaspoon = 12 servings ........(2)
So, First we find the ratio
Ratio is
So to equal the ratio multiply (1) by
cups +
teaspoon =
servings
cups +
teaspoon = 12 servings
On comparing with (2),
The value of x is .
Therefore, The broth do we need is cups.
So, Option A is correct.