Answer:
x = -2, y = -2
Step-by-step explanation:
Your goal is to try and cancel out a variable. I want to get rid of y so i subtracted the first equation from the second one.
After that I solve for x and got x=-2.
I used x=-2 and plugged it back into either of the equation to solve for y.
Given the System of Equations:
The exercise asks for solving it graphically. Then, in this case, you need to graph both lines in order to determine the solution of the system.
In order to graph it, you can find the x-intercepts and the y-intercepts:
1. It is important to remember the Slope-Intercept Form of the equation of a line:
Where "m" is the slope of the line and "b" is the intercept.
In this case, you can identify that the y-intercept of the first line is:
And the y-intercept of the second line is:
2. By definition, the value of "y" is zero when the line intersects the x-axis.
Then, you need to substitute the following value of "y" into each equation and then solve for "x", in order to find the x-intercept of each line:
- For the first line, you get:
- For the second line, you get:
3. Now you know that the first line passes through these two points:
And the second line passes through these two points:
4. Knowing those points, you can graph the lines:
Notice that the line intersect each other at
Answer:
So 67 degrees is one value that we can take the sine of such that is equal to cos(23 degrees).
(There are more values since we can go around the circle from 67 degrees numerous times.)
Step-by-step explanation:
You can use a co-function identity.
The co-function of sine is cosine just like the co-function of cosine is sine.
Notice that cosine is co-(sine).
Anyways co-functions have this identity:
or
You can prove those drawing a right triangle.
I drew a triangle in my picture just so I can have something to reference proving both of the identities I just wrote:
The sum of the angles is 180.
So 90+x+(missing angle)=180.
Let's solve for the missing angle.
Subtract 90 on both sides:
x+(missing angle)=90
Subtract x on both sides:
(missing angle)=90-x.
So the missing angle has measurement (90-x).
So cos(90-x)=a/c
and sin(x)=a/c.
Since cos(90-x) and sin(x) have the same value of a/c, then one can conclude that cos(90-x)=sin(x).
We can do this also for cos(x) and sin(90-x).
cos(x)=b/c
sin(90-x)=b/c
This means sin(90-x)=cos(x).
So back to the problem:
cos(23)=sin(90-23)
cos(23)=sin(67)
So 67 degrees is one value that we can take the sine of such that is equal to cos(23 degrees).
