What are the solutions to the system of equations? y=2x^2−6x+3 y=2x+3
1 answer:
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Answer:
2 and 5
Step-by-step explanation:
The slope-intercept form of a line is y=mx-b where m is slope and b is y-intercept.
The point-slope form of a line is y-y1=m(x-x1) where m is the slope and (x1,y1) is a point on the line.
The standard form a line is ax+by=c.
So anyways parallel lines have the same slope.
So if we are looking for a line parallel to 3x-4y=7 then we need to know the slope of this line so we can find the slope of our parallel line.
3x-4y=7
Goal: Put into slope-intercept form
3x-4y=7
Subtract 3x on both sides:
-4y=-3x+7
Divide both sides by -4:
Simplify:
So the slope of this line is 3/4. So our line that is parallel to this one will have this same slope.
So we know our line should be in the form of .
To find b we will use the point that is suppose to be on our new line here which is (x,y)=(-4,-2).
So plugging this in to solve for b now:
so the equation of our line in slope-intercept form is
So that isn't option 1 because the slope is different. That was the only option that was in slope-intercept form.
The standard form of a line is ax+by=c and we have 2 options that look like that.
So let's rearrange the line that we just found into that form.
Clear the fractions because we only want integer coefficients by multiplying both sides by 4.
This gives us:
Subtract 3x on both sides:
I don't see this option either.
Multiply both sides by -1:
I do see this as a option. So far the only option that works is 2.
Let's look at point slope form now.
We had the point that our line went through was (x1,y1)=(-4,-2) and the slope,m, was 3/4 (we found this earlier).
y-y1=m(x-x1)
Plug in like so:
y-(-2)=3/4(x-(-4))
y+2=3/4 (x+4)
So option 5 looks good too.