solve my system of equation with full steps
3x+4y=29
2x–5y=-19
6,-1
To solve the system of equations, we will use the method of elimination. Here are the steps:
1. We have the following system of equations:
Equation 1: 3x + 4y = 29
Equation 2: 2x - 5y = -19
2. Multiply Equation 1 by 5 and Equation 2 by 4 to make the coefficients of y's the same in both equations:
Equation 1: 15x + 20y = 145
Equation 2: 8x - 20y = -76
3. Add Equation 1 and Equation 2 to eliminate the y variable:
(15x + 20y) + (8x - 20y) = 145 + (-76)
15x + 8x + 20y - 20y = 145 - 76
23x + 0 = 69
23x = 69
4. Solve for x by dividing both sides of the equation by 23:
23x / 23 = 69 / 23
x = 3
5. Substitute the value of x back into Equation 1 (or Equation 2) to solve for y:
3(3) + 4y = 29
9 + 4y = 29
4y = 29 - 9
4y = 20
6. Solve for y by dividing both sides of the equation by 4:
4y / 4 = 20 / 4
y = 5
7. The solution to the system of equations is x = 3 and y = 5.
So, the system of equations is solved by finding x = 3 and y = 5.
Multiply I eq by 2 and II by 3
6x+8y=58
6x-15y=-57. Subtract II eq from I. Signs of II eq will change:-6x+15y=57.
Thus, 8y+15y=58+57 Or 23y=115
or y=115/23=5.
Now substitute this in any original eq:
3x-4x5=29 or 3x=29-20=9, hence x=9/3=3