<h3>
Solution (1):</h3>
<u>Given:</u>
<u>Multiplying y = 3x - 5 by 2:</u>
y = -6x - 5
y = -6x - 5
<u>Adding both equations:</u>
<u>Dividing 3 both sides:</u>
<u>Substitute the value of y into any equation.</u>
- y = -6x - 5
- => -5 = -6x - 5
- => 0 = -6x
<u>Divide -6 both sides.</u>
<h3>
Solution (2):</h3>
<u>Given:</u>
<u>Add both the equations.</u>
y = -8x + 7
<u>Divide 2 both sides.</u>
- 2y = -2
- => 2y/2 = -2/2
- => y = -1
<u>Substitute the value of y into any equation.</u>
<u>Add 9 both sides.</u>
- => -1 + 9 = 8x - 9 + 9
- => 8 = 8x
<u>Divide 8 both sides.</u>
<h3>
Solution (3):</h3>
<u>Given:</u>
<u>Reorganize the first equation.</u>
- -x + 6y = 21
- => 6y = x + 21
<u>Multiply the first equation by 5.</u>
y = -5x + 12
y = -5x + 12
<u>Add both the equations.</u>
<u>Divide 31 both sides.</u>
- 31y = 117
- => 31y/31 = 117/31
- => y = 117/31
<u>Substitute the value of y into any equation.</u>
- -x + 6y = 21
- => -x + 6(117/31) = 21
- => -x + 702/31 = 651/31
<u>Subtract 702/31 both sides.</u>
- => -x = 651/31 - 702/31
- => -x = -51/31
- => x = 51/31
Remember, you can do anything to an equation as long as you do it to both sides
4+x-17=22
add like terms
x+4-17=22
x-13=22
add 13 to both sides
x+13-13=22+13
x+0=35
x=35
To determine the measure of the angle with the cosine value equal to 0.208, we have to use the inverse trigonometric functions. In this number, we have the arccosine which is also written below.
cos⁻¹(0.208) = 77.9948⁰
Therefore, the measure of the angle with cosine equal to 0.208 rounded to the nearest thousandth is <em>77.995⁰</em>.
Answer: 21 dollars was his bill before the tip
Step-by-step explanation: 4.20 is 20% of what he paid with no tip included. This means you can set up an equation like this.
4.20 = .2x This means that $4.20 is (is means =) 20% of (of means multiply) x (which is the unknown factor).