For the following system of equations, what is the x-value of the solution?

Question

–x + 2y = 6 6y = x + 18
(1 point)
–18 0 –6 3

Answer 1

To find the x-value of the solution for the given system of equations, we need to solve the equations simultaneously.

First, let's solve the second equation for x:
6y = x + 18
Subtract 18 from both sides:
x = 6y - 18

Now substitute this value of x into the first equation:
–x + 2y = 6
-(6y - 18) + 2y = 6
Multiply -1 by each term inside the parentheses:
-6y + 18 + 2y = 6
Combine like terms:
-4y + 18 = 6
Subtract 18 from both sides:
-4y = -12
Divide both sides by -4:
y = 3

Now, substitute this value of y back into the second equation to find x:
6y = x + 18
6(3) = x + 18
18 = x + 18
Subtract 18 from both sides:
0 = x

The x-value of the solution is 0.

Answer 2

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?
(1 point)
20° 35° 50° 65°

Answer 3

Let's assume the measure of angle Y is y.

According to the information given in the problem, the measure of angle X is 30 less than twice the measure of angle Y. So, we can write the equation:

X = 2Y - 30

We also know that the sum of the measures of angle X and angle Y is 90 degrees. So, we can write another equation:

X + Y = 90

Now, let's substitute the value of X from the first equation into the second equation:

(2Y - 30) + Y = 90
3Y - 30 = 90
3Y = 120
Y = 40

Now, substitute the value of Y back into the first equation to find the measure of angle X:

X = 2(40) - 30
X = 80 - 30
X = 50

Therefore, the measure of angle X is 50°.

Answer 4

The yearbook club is having a bake sale to raise money for the senior class. Large cupcakes are sold for $1.25 each and small cupcakes are sold for $0.75 each. If 105 cupcakes were sold for a total amount of $109.75, how many large cupcakes did the yearbook club sell?
(1 point)
43 55 62 16

Answer 5

Let's assume the number of large cupcakes sold is L and the number of small cupcakes sold is S.

According to the information given in the problem, each large cupcake is sold for $1.25, so the total revenue from selling large cupcakes is 1.25L.
Similarly, each small cupcake is sold for $0.75, so the total revenue from selling small cupcakes is 0.75S.

The total number of cupcakes sold is given as 105, so we can write the equation:
L + S = 105

The total revenue from selling all the cupcakes is given as $109.75, so we can write another equation:
1.25L + 0.75S = 109.75

Now, we have a system of two equations with two variables. We can solve this system to find the values of L and S.

Using the substitution method, we can solve the first equation for S:
S = 105 - L

Substituting this value of S into the second equation:
1.25L + 0.75(105 - L) = 109.75
1.25L + 78.75 - 0.75L = 109.75
0.5L + 78.75 = 109.75
0.5L = 109.75 - 78.75
0.5L = 31
L = 31 / 0.5
L = 62

Therefore, the yearbook club sold 62 large cupcakes.

Answer 6

Solve the following system of equations using substitution. What is the value of y?
2x + 3y = 105 x + 2y = 65
(1 point)
15 25 40 65

Answer 7

To solve the system of equations using substitution, we'll solve one equation for one variable and substitute it into the other equation.

Let's solve the second equation for x:
x + 2y = 65
x = 65 - 2y

Now, substitute this value of x into the first equation:
2(65 - 2y) + 3y = 105
130 - 4y + 3y = 105
Combine like terms:
-y + 130 = 105
Subtract 130 from both sides:
-y = -25
Divide both sides by -1:
y = 25

The value of y is 25.