3x-4y=8
5x+3y=23
Based on the above system of 2-equations, which of the following values (x+y) equal?
10, 8, 7, or 5
To find which of the given values of (x+y) is equal, we need to solve the given system of equations using either substitution or elimination method. Let's use the elimination method here.
First, we need to eliminate one variable by multiplying both equations by suitable constants so that the coefficients of one of the variables are opposites. In this case, we can multiply the first equation by 5 and the second equation by 3 to get opposite coefficients for 'y':
(5)(3x - 4y) = (5)(8) => 15x - 20y = 40
(3)(5x + 3y) = (3)(23) => 15x + 9y = 69
Now we can eliminate 'x' by subtracting the second equation from the first equation:
(15x - 20y) - (15x + 9y) = 40 - 69
15x - 20y - 15x - 9y = -29
-29y = -29
y = 1
Now that we have found the value of 'y', we can substitute it back into one of the original equations to solve for 'x'. Let's choose the first equation:
3x - 4(1) = 8
3x - 4 = 8
3x = 12
x = 4
So, the solution to the system of equations is x = 4 and y = 1.
To find which value of (x+y) is equal, we substitute the values of x and y into (x+y):
(x + y) = (4 + 1) = 5
Therefore, the value of (x + y) that is equal to one of the given options is 5.
15 x -20 y = 40
15 x + 9 y = 69
-------------------subtract
-29 y = -29
y = 1
3 x - 4 = 8
3 x = 12
x = 4
x+y = 4 + 1 = 5