if 5x + 7y = 18 and 2x - 4y = 6, what is the value of 7x + 3y?
a. 7
b. 12
c. 19
d. 24
e. 31
take the 2nd and divide by 2
x - 2y = 3
x = 2y+3
plug that into the first
5(2y+3) + 7y = 18
10y+15+7y=18
25y=25
y=1
then x = 2(1) + 3 = 5
now that we have x=5, and y=1
evaluate 7x+3y
35
To find the value of 7x + 3y, we need to solve the system of equations given:
1) 5x + 7y = 18
2) 2x - 4y = 6
We can use the method of substitution or the method of elimination to solve this system of equations.
Let's use the method of elimination to eliminate one variable and solve for the other.
Multiplying equation 2 by 7, we get:
7(2x - 4y) = 7(6)
14x - 28y = 42
Now, we can add equation 1 and the modified equation 2 together to eliminate the x variable:
(5x + 7y) + (14x - 28y) = 18 + 42
19x - 21y = 60
Next, we need to solve this new equation for either x or y. Let's solve it for x:
19x = 60 + 21y
x = (60 + 21y) / 19
Now, substitute this expression for x into one of the original equations. Let's use equation 1:
5((60 + 21y) / 19) + 7y = 18
Now, we can solve this equation for y:
Multiply both sides of the equation by 19 to eliminate the fraction:
5(60 + 21y) + 133y = 342
300 + 105y + 133y = 342
238y = 42
y = 42 / 238
y = 1/6
Now that we have the value of y, we can substitute it back into equation 1 or 2 to find the value of x:
5x + 7(1/6) = 18
5x + 7/6 = 18
5x = 18 - 7/6
5x = 108/6 - 7/6
5x = 101/6
x = (101/6) / 5
x = 101/30
Finally, we can calculate the value of 7x + 3y using the values we found for x and y:
7(101/30) + 3(1/6)
= 707/30 + 3/6
= 707/30 + 15/30
= 722/30
= 361/15
Therefore, the value of 7x + 3y is 361/15.
But none of the answer choices match this value, so there might be an error in the problem.