Solve the system.4x+3y=11 and3x -2y=4
x= -2 and y = -1
678/987
To solve the system of equations 4x + 3y = 11 and 3x - 2y = 4, we will use the method of elimination or substitution.
Method 1: Elimination
Step 1: Multiply the first equation by 3 and the second equation by 4 to create equal coefficients for x.
Equation 1: 4(4x + 3y) = 4(11) -> 12x + 9y = 44
Equation 2: 3(3x - 2y) = 3(4) -> 9x - 6y = 12
Step 2: Multiply equation 1 by 2 and equation 2 by -3 to create equal coefficients for y.
Equation 1: 2(12x + 9y) = 2(44) -> 24x + 18y = 88
Equation 2: -3(9x - 6y) = -3(12) -> -27x + 18y = -36
Step 3: Add equation 1 and equation 2 to eliminate y.
(24x + 18y) + (-27x + 18y) = 88 + (-36)
-3x = 52
x = -52/3
Step 4: Substitute the value of x into one of the original equations to solve for y.
Using equation 1: 4(-52/3) + 3y = 11
-208/3 + 3y = 11
3y = 11 + 208/3
3y = 43/3
y = 43/9
Therefore, the solution to the system of equations is x = -52/3 and y = 43/9.
Now, let's move on to the next question:
To find the value of 678/987, you can simply divide 678 by 987.
Step 1: Divide 678 by 987:
678 ÷ 987 = 0.686781609...
Therefore, the value of 678/987 is approximately 0.6868 (rounded to four decimal places).