These problems are called systems of equations. Basically you have two linear equations and you need to find the values for x and y. In other words, all these equation are lines and our answer will be the exact point that the pair of lines intersect. For example, if we get x=1 and y=2 the lines will intersect at point (1,2). Now that you have some background knowledge here comes the tricks and tactics kid.
We know that we can solve one variable equation easily. For example...
x+1=2
x=1 obviously
Cause we have two variables x and y it is not possible to find a solution. For example, in the equation x+y=10, x=1 when y=9 and x=2 when y=8. There is not correct answer.
So what can we do? We have to make a two variable equation into a one variable equation.
There are two ways to do this: substitution and elimination. I will create a sample problem and then solve it using both methods.
x+y=2
2y-y=1
3)
-3x-5y=-7 -----> -12x-20y=-28
-4x-3y=-2 ------> -12x-9y=-6
-12x-20y=-28
-(-12x-9y=-6)
---------------------
-11y=-22
y=2
-3x-5(2)=-7
-3x=3
x=-1
4) 8x+4y=12 ---> 24x+12y=36
7x+3y=10 ---> 28x+12y=40
28x+12y=40
-(24x+12y=36)
---------------------
4x=4
x=1
8(1)+4y=12
4y=4
y=1
5) 4x+3y=-7
-2x-5y=7 ----> -4x-10y=14
4x+3y=-7
+(-4x-10y=14)
-------------------
-7y=7
y=-1
4x+3(-1)=-7
4x=-4
x=-1
6) 8x-3y=-9 ---> 32x-12y=-36
5x+4y=12 ---> 15x+12y=36
32x-12y=-36
+(15x+12y=36)
--------------------
47x=0
x=0
8(0)-3y=-9
-3y=-9
y=3
7)-3x+5y=-2
2x-2y=1 ---> x-y=1/2 ----> x=y+1/2
-3(y+1/2)+5y=-2
-3y-1.5+5y=-2
2y=-0.5
y=0.25
2x-2(0.25)=1
2x=1.5
x=0.75
Answer:
1. 50%
2. 3%
3. 20%
4. 200%
Step-by-step explanation:
Here, we want to find the worth of each coin as a percentage of $1
We simply divide the worth by $1 and multiply by 100%
$1 is same as 100 cents
Thus;
1. 50 cent
= 50/100 * 100% = 50%
2. 3 cents
= 3/100 * 100% = 3%
3. 20 cents
= 20/100 * 100% = 20%
4. $2
= 2/1 * 100% = 200%
Hello :
<span> y=-6(2.5-x)(x-5.5) = -6(2.5x -13.75 -x² +5.5x)
y = -6(-x²+8x -13.75)
y = 6x²-48x+82.5
note :
if f(x) = ax²+bx +c the vertex is the point : ( -b/2a ; f(-b/2a))
a=6 b=-48 c = 82.5 .......calculate
-b/2a = -(-48)/2(6)= 4
f(4) =6(4)²-48(4)+82.5 =96 - 192 +82.5 = -13.5</span>
Answer:
Step-by-step explanation:
Hi there!
<u>What we need to know:</u>
- Linear equations are typically organized in slope-intercept form:
where m is the slope and b is the y-intercept (the value of y when x is 0) - Perpendicular lines always have slopes that are negative reciprocals (ex. 3 and -1/3, 5/6 and -6/5, etc.)
<u>1) Determine the slope (m)</u>
y=x-9
Rewrite the equation
y=1x-9
Now, we can identify clearly that the slope of the line is 1. The negative reciprocal of 1 is -1, so therefore, the slope of a perpendicular line would be -1. Plug this into :
<u />
<u>2) Determine the y-intercept (b)</u>
Plug in the given point (7,9) and solve for b
Add 7 to both sides to isolate b
Therefore, the y-intercept is 16. Plug this back into :
I hope this helps!
Answer (the system of equations input doesn't work, so there is no brace):
x = 1.5y
x + y =800
Step-by-step explanation:
First, identify the vital information:
- 800 total students
- 1.5 times as many boys as girls
So, if x = number of boys and y = number of girls, we can agree that:
x = 1.5y
And because there are 800 kids in total, we can agree that:
x + y = 800
There are 320 girls and 480 boys. (see below)
Since you have the value of x, 1.5y, you can plug-in the value:
x + y = 800
1.5 + y = 800
2.5y = 800
y = 320 girls
Plug-in the y-value into the equation for the number of boys:
x = 1.5y
x = 1.5(320)
x = 480 boys
To double-check:
320 + 480 = 800 ☺
