1. What is the solution of the system?
4x + 3y = 12
7x + 5y = 26
A. (18, 20)
B. (18, -20)
C. (-20, 18)
D. (20, 18)
4x+3y=12
7x+5y=26
B:18,-20
Well, I guess the solution to this system is not to let X and Y argue with each other. It seems like they have a lot of unresolved issues. But if we actually do the math, it looks like the answer is Option A: (18, 20). So, let's hope X and Y can find some common ground and live happily ever after.
To solve the system of equations, we can use the method of elimination. The goal is to eliminate one variable by adding or subtracting the two equations.
Step 1: Multiply the first equation by 7 and the second equation by 4 to make the coefficients of x in both equations the same:
7(4x + 3y) = 7(12)
4(7x + 5y) = 4(26)
Simplifying gives:
28x + 21y = 84
28x + 20y = 104
Step 2: Now subtract the second equation from the first equation to eliminate x:
(28x + 21y) - (28x + 20y) = 84 - 104
Simplifying gives:
y = -20
Step 3: Substitute the value of y back into one of the original equations. Let's use the first equation:
4x + 3(-20) = 12
Simplifying gives:
4x - 60 = 12
Step 4: Add 60 to both sides:
4x = 72
Step 5: Divide both sides by 4 to solve for x:
x = 18
Therefore, the solution of the system is (18, -20), which corresponds to option B.
To find the solution of the system of equations, we can use the method of substitution or the method of elimination. Let's use the method of substitution.
1. Solve one of the equations for one variable in terms of the other variable.
Let's solve the first equation for x:
4x + 3y = 12
Subtract 3y from both sides:
4x = 12 - 3y
Divide both sides by 4:
x = (12 - 3y) / 4
2. Substitute this expression for x into the second equation.
7x + 5y = 26
Replace x with (12 - 3y) / 4:
7((12 - 3y) / 4) + 5y = 26
3. Simplify and solve for y.
Multiply both sides by 4 to clear the fraction:
7(12 - 3y) + 20y = 104
Distribute the 7:
84 - 21y + 20y = 104
Combine like terms:
- y + 84 = 104
Subtract 84 from both sides:
-y = 20
Multiply both sides by -1 to isolate y:
y = -20
4. Now, substitute the value of y back into the first equation to solve for x:
4x + 3(-20) = 12
4x - 60 = 12
Add 60 to both sides:
4x = 72
Divide both sides by 4:
x = 18
Therefore, the solution to the system of equations is (x, y) = (18, -20).
So, the correct answer is B. (18, -20).
multiply first equation by 5
and
the second equation by 3
20 x + 15 y = 60
21 x + 15 y = 78
------------------subtract
-1 x = - 18
so
x = 18
now go back and find y