To solve with Elimination:
Write the equations under one another, like this:
2x - y = -1
+ 3x + 4y = 26
Ideally, we would like for one of the variables to be eliminated when we add vertically (straight down). But if we add them as they are this does not happen. We must manipulate one of the equations so that it will happen. Again, you can try to eliminate either x or y. I always look for a term that has a coefficient of 1 (or negative 1). So, let's use that y from the first equation again.
If the coefficient of the y in the other equation is POSITIVE 4, then I need the coefficient from the first equation to be its opposite, NEGATIVE 4. To do this, simply multiply the first equation by 4, this will create MAGIC!
4( 2x - y = -1)
+ 3x + 4y = 26
Be certain to Distribute across the entire first equation, so multiply all three terms by 4.
8x - 4y = -4
+ 3x + 4y = 26
Now add straight down (vertically). The y term will be eliminated.
11x = 22
Divide both sides of the equation by 11.
x = 2
Almost there! Now, substitute the 2 in for x in either of the original equations. Either one will work. I'm gonna use the second equation.
3x + 4y = 26
3(2) + 4y = 26
6 + 4y = 26
Subtract 6 from both sides of the equation.
4y = 20
Divide both sides of the equation by 4.
y = 5
That's it! There it is again. Put it all together. If x = 2 and y = 5, then the solution is the ordered pair, (2,5).
Answer:
Let P(t) = population t years after 2010
= 45230e0.02t
Population in 2030 = P(20)
= 45230e0.4≈ 6747
8 million 3 hundred sixty-four thousand nine hundred eighty-seven
Answer:
b. y = −0.5x + 5.5
Step-by-step explanation:
Well first we need to find the slope of line CD.
To do that we'll use the following formula,

We'll use the points (1,1) and (3,5)
So y2 is 5 y1 is 1 so 5-1 = 4
3-1 = 2
<u>Slope = 2x</u>
If the slope of line CD is 2x we can cross out choices C and D.
Two lines that are perpendicular to each other have reciprocal slopes,
meaning is the slope of line CD is 2 then its perpendicular lines slope should be -.5.
If the perpendicular line goes through point (-1,6), the y intercept would be, 5.5.
Look at the image below ↓
<em>Thus,</em>
<em>the answer is option b. y = −0.5x + 5.5.</em>
<em>Hope this helps :)</em>