A)
Multiple Choice
For the following system of equations, what is the x-value of the solution?
–x + 2y = 6
6y = x + 18
(1 point)
–18
0
–6
3
To find the x-value of the solution, we need to solve the given system of equations.
First, let's rearrange the equations to solve for x in terms of y:
–x + 2y = 6
x = 2y - 6
6y = x + 18
x = 6y - 18
Now we can set the two expressions for x equal to each other and solve for y:
2y - 6 = 6y - 18
2y - 6y = - 18 + 6
-4y = -12
y = -12 / -4
y = 3
Now that we have the value of y, we can substitute it back into either equation to solve for x:
x = 2y - 6
x = 2(3) - 6
x = 6 - 6
x = 0
Therefore, the x-value of the solution is 0.
A)
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°
Let's set up an equation using the given information.
Let the measure of angle Y be represented by y.
Then, according to the problem, the measure of angle X is 30 less than twice the measure of angle Y:
X = 2Y - 30
We also know that the sum of the measures of angle X and angle Y is 90:
X + Y = 90
Now, we can substitute the expression for X from the first equation into the second equation:
(2Y - 30) + Y = 90
Combine like terms:
3Y - 30 = 90
Add 30 to both sides of the equation:
3Y = 120
Divide both sides by 3:
Y = 40
Now, we can 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°.
A)
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
Let's set up two equations to represent the information given:
L = number of large cupcakes sold
S = number of small cupcakes sold
The total number of cupcakes sold is given as 105:
L + S = 105
The total amount of money earned from the sale is $109.75:
1.25L + 0.75S = 109.75
We can use substitution or elimination to solve this system of equations. Let's use substitution:
From the first equation, we can express S in terms of L:
S = 105 - L
Substitute this expression for S into the second equation:
1.25L + 0.75(105 - L) = 109.75
Simplify:
1.25L + 78.75 - 0.75L = 109.75
Combine like terms:
0.5L + 78.75 = 109.75
Subtract 78.75 from both sides:
0.5L = 31
Divide both sides by 0.5:
L = 62
Therefore, the yearbook club sold 62 large cupcakes.
A)
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
To solve the system of equations using substitution, we can 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 we can substitute this expression for x into the first equation:
2(65 - 2y) + 3y = 105
Simplify:
130 - 4y + 3y = 105
Combine like terms:
-4y + 3y = 105 - 130
Simplify:
-y = -25
Now, let's solve for y by multiplying both sides of the equation by -1:
y = 25
Therefore, the value of y is 25.