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:
If you shoot the bullet off the back of the car , the bullet will still be moving away from you and the gun at 1,000 mph, but now the speed of the train will subtract from the speed of the bullet. Relative to the ground, the bullet will not be moving at all, and it will drop straight to the ground.
Step-by-step explanation:
Answer: 12 miles
Step-by-step explanation:
Hi, to answer this question we have to write a growth equation.
Total miles = 8 (1 +0.05)^9 = 12.41 =12 miles
Where 8 is the initial miles she run, since is increasing each week by 5% we have to multiply it by 1+ percent increase rate in decimal form (1+0.05) to 9th power (number of weeks)
She will run 12 miles in 9 weeks.
Well I figured it out and I came up with 13 square inches. you can find this out by doing the square root of 169. I hope this help :).
