Eliminate 5x-19=2y
3y+ 18=4x under simultaneous linear equation
No
To solve the given system of simultaneous linear equations:
Equation 1: 5x - 19 = 2y
Equation 2: 3y + 18 = 4x
Step 1: We need to eliminate one variable from the given equations. Let's eliminate x by finding a common coefficient for it in both equations.
Multiply Equation 1 by 2, and Equation 2 by 4 to make the coefficients of the x term equal:
Equation 1: 2(5x - 19) = 2(2y)
10x - 38 = 4y (multiply)
Equation 2: 4(3y + 18) = 4(4x)
12y + 72 = 16x (multiply)
Now we have the equations:
10x - 4y - 38 = 0
16x - 12y - 72 = 0
Step 2: Now, we can either use the method of substitution or elimination to solve the system. Let's use the method of elimination:
Multiply Equation 1 by 3 and Equation 2 by 2 to make the coefficients of the y term equal:
Equation 1: 3(10x - 4y - 38) = 3(0)
30x - 12y - 114 = 0 (multiply)
Equation 2: 2(16x - 12y - 72) = 2(0)
32x - 24y - 144 = 0 (multiply)
Now we have the equations:
30x - 12y - 114 = 0
32x - 24y - 144 = 0
Step 3: Now, we will subtract Equation 1 from Equation 2 to eliminate y:
(32x - 24y - 144) - (30x - 12y - 114) = 0
32x - 24y - 144 - 30x + 12y + 114 = 0
(32x - 30x) + (-24y + 12y) - 144 + 114 = 0
2x - 12 = 0
Simplify the equation:
2x = 12
x = 12/2
x = 6
Step 4: Substitute the value of x back into either Equation 1 or Equation 2 to solve for y. Let's use Equation 1:
5x - 19 = 2y
5(6) - 19 = 2y
30 - 19 = 2y
11 = 2y
y = 11/2
y = 5.5
Therefore, the solution to the given system of simultaneous linear equations is x = 6 and y = 5.5.
Have not seen the answer
impatient much?
Rearrange to get
5x - 2y = 19
4x - 3y = 18
Now do some multiplication to eliminate y:
15x - 6y = 57
8x - 6y = 36
Now subtract to get
7x = 21
I expect you can finish it off from here ...