Solve the following system using elimination:
{7 x + 2 y = -19 | (equation 1)
{2 y - x = 21 | (equation 2)
Add 1/7 × (equation 1) to equation 2:
{7 x + 2 y = -19 | (equation 1)
{0 x+(16 y)/7 = 128/7 | (equation 2)
Multiply equation 2 by 7/16:
{7 x + 2 y = -19 | (equation 1)
{0 x+y = 8 | (equation 2)
Subtract 2 × (equation 2) from equation 1:
{7 x+0 y = -35 | (equation 1)
{0 x+y = 8 | (equation 2)
Divide equation 1 by 7:
{x+0 y = -5 | (equation 1)
{0 x+y = 8 | (equation 2)
Collect results:
Answer: {x = -5, y = 8
The triangle has one angle of 100 degrees, and the other two are equal.
We know that the angles of a triangle always add up to 180. To find the measurement of angle 1 and 2, let's solve for this equation.
2x + 100 = 180, where x=angle 1 = angle 2. Subtract 100 from both sides
2x = 80 Divide both sides by 2
x = 40
Answer:
mx -y = 4m -7
Step-by-step explanation:
Standard form is ...
ax +by = c
where a, b, c are mutually prime integers and a > 0.
If we assume m > 0, then we need to collect the variable terms on the right side of the equation, so the coefficient of x will be positive.
y -7 = mx -4m . . . . eliminate parentheses
-7 = mx -y -4m . . . . subtract y
4m -7 = mx -y . . . . . add 4m
mx -y = 4m -7 . . . . . . standard form
Answer:
$9000 at 4$
and
$10000 at 8%
Step-by-step explanation:
Let's assume that "x" is the amount deposited in the 4% account and "y" is the amount deposited in the 8% account.
Recall the formula for interest as : 
where I is the interest, R is the annual rate of interest and t is the number of years.
Since there are two investments, we need to add both interests at the end of the one year: I1 = x (0.04) (1) = 0.04 x and I2 = y (0.08) (1) = 0.08 y
Total Interest = Interest (from the 4% account) + Interest (from the 8% account)
Total Interest = $1160 = 0.04 x + 0.08 y
we also know that the total invested (x + y) adds to $19,000, that is:
$19,000 = x + y
Then we can solve these system of two equations by substitution, for example solving for y in the second equation and using the y substitution in the first equation;
y = 19000 - x
1160 = 0.04 x + 0.08 (19000 - x)
1160 = 0.04 x + 1520 - 0.08 x
0.08 x - 0.04 x = 1520 - 1160
0.04 x = 360
x = 360/0.04 = $9000
Then the other investment was : y = $19000 - $9000 = $10000
All of them are 3.14
I got them all right on I ready :)))
