Their are 2 main methods of solving 2 equations with 2 variables:
1) SUBSTITUTION
2) ELIMINATION
I'll show you both:
1) y = 2x + 160
y = - 3x + 208
plug what y is equal to in 1st equation into the y of the 2nd:
2x + 160 = -3x + 208
2x + 3x + 160 = -3x + 3x + 208
5x + 160 -160 = 208 - 160
5x = 48
5x/5 = 48/5
x = 48/5 = 9 3/5
now plug that x into either one of the original equations: y = -3x + 208 = -3(48/5) + 208
y = -144/5 + 208 = 1040/5 - 144/5 = 896/5
y = 179 1/5
2) add the whole equations together so as to cancel out one of the variables:
I'm choosing to eliminate the y, so we need y-y to remove the y's, I'll multiply the whole 2nd equation by -1 to make that -y
-1 (y = - 3x + 208)
-y = 3x - 208
So set it up like:
y = 2x + 160
-[y = 3x - 208]
---------------------
0 = 5x - 48
0+48 = 5x -48 +48
5x = 48
5x/5 = 48/5
x = 48/5
plug that x value into one of the original equations: y = 2x + 160 = 2(48/5) + 160
y = 96/5 + 160 = 96/5 + 800/5 = 896/5
y = 179 1/5
SO WE GOT THE SAME VALUES BOTH WAYS.
WHEN YOU SEE FUTURE PROBLEMS LIKE THESE, SOME WILL BE QUICKER BY ELIMINATION AND OTHERS BY SUBSTITUTION
Answer:
The product of 1.304 and 1,000,000 is 1,304,000 because the decimal point in 1.304 moves 6 places to the right.
Step-by-step explanation:
<span>A line passes through the point (–7, 5) and has a slope of 1/5.
So this line would be y=1/5x+b
If we substitute x and y into this </span>formula
We can get b=5+7/5=32/5
Then y=1/5x+32/5
If x=0, then y=32/5
So another point on this line is (0,32/5)
Answer:
Given: The following system:
4x + y − 2z=18 ......[1]
2x-3y+3z = 21 ......[2]
x-3y=6 ......[3]
we can write equation [3] as;
3y = x-6 ......[4]
Multiply by 3 in equation [1] to both sides of an equation we get,
or
12x+3y-6z=54 ......[5]
Substituting the equation [4] in [2] and [5] we get;
2x-(x-6)+3z=21 or
2x-x+6+3z=21
Simplify:
x+3z=15 .....[6] [combine like terms]
12x+x-6-6z =54
Simplify:
13x-6z=60 ......[7] [Combine like terms]
On Solving equation [6] and [7] simultaneously,
x+3z=15
13x-6z=60
we get the value of x
i.e, x=6
Substitute the value of x in equation x+3z=15 we get
6+3z=15 or
3z=9
Simplify:
z=3
Also, substitute the value of x=6 in equation [3] we get the value of y;
x-3y=6
6-3y=6 or
-3y = 0
Simplify:
y = 0
Therefore, the solution to the system of three linear equation is, (6, 0 , 3)
The answer is 10 10 students liked scary movies out of 35
