Question

-x + 2y = 6
6y = x + 18

Answer 1

the sum of the measures of angle x and angle y is 90. if the measure of angle x is 30 less than twice the measure of angle y what is the measure of angle x

Answer 2

large cupcakes are sold for $1.25 each, and small cupcakes are sold for $0.75 each. if 105 cupcakes wee sold for $109.75 how many were large.

Answer 3

To solve this system of equations, we'll notice that both equations are in terms of x and y. Thus, by isolating x in equation 2, we can substitute it into equation 1 and solve for y.

Starting with equation 2:
6y = x + 18

We can rearrange this equation to isolate x:
x = 6y - 18

Now we substitute this value of x into equation 1:
-x + 2y = 6
-(6y - 18) + 2y = 6
-6y + 18 + 2y = 6
(-6y + 2y) + 18 = 6
-4y + 18 = 6
-4y = 6 - 18
-4y = -12
y = -12 / -4
y = 3

Now that we have the value of y, we can substitute it back into equation 2 to solve for x:
6y = x + 18
6(3) = x + 18
18 = x + 18
x = 0

Therefore, the solution to the system of equations is x = 0 and y = 3.

Answer 4

Let's represent the measure of angle y as "y".

According to the problem, the measure of angle x is 30 less than twice the measure of angle y. In equation form, this can be written as:

x = 2y - 30

We also know that the sum of the measures of angle x and angle y is 90 degrees:

x + y = 90

Now we can substitute the value of x from the first equation into the second equation:

(2y - 30) + y = 90

Combining like terms:

3y - 30 = 90

Adding 30 to both sides:

3y = 120

Dividing by 3:

y = 40

Therefore, the measure of angle x is:

x = 2y - 30 = 2(40) - 30 = 80 - 30 = 50

The measure of angle x is 50 degrees.

Answer 5

Let's represent the number of large cupcakes as "L" and the number of small cupcakes as "S".

According to the problem, large cupcakes are sold for $1.25 each and small cupcakes are sold for $0.75 each. The total number of cupcakes sold is 105, and the total amount of money collected from the sales is $109.75.

We can set up a system of equations to represent this information:

L + S = 105 ----(equation 1)
1.25L + 0.75S = 109.75 ----(equation 2)

To solve this system of equations, we'll multiply equation 1 by 0.75 to get:

0.75L + 0.75S = 78.75 ----(equation 3)

Now we can subtract equation 3 from equation 2 to eliminate the variable S:

(1.25L + 0.75S) - (0.75L + 0.75S) = 109.75 - 78.75
0.5L = 31
L = 31 / 0.5
L = 62

Therefore, there were 62 large cupcakes sold.