Question
solve the system with elimination 5x-4y=-27 and 4x+3y=28
Answers
GPT 3.5
To solve the system using elimination, we will multiply the first equation by 4 and the second equation by 5 to create opposite coefficients for the x-term.
Original equations:
1) 5x - 4y = -27
2) 4x + 3y = 28
Multiply equation 1 by 4:
4(5x - 4y) = 4(-27)
20x - 16y = -108
Multiply equation 2 by 5:
5(4x + 3y) = 5(28)
20x + 15y = 140
New system:
3) 20x - 16y = -108
4) 20x + 15y = 140
Next, subtract equation 3 from equation 4 to eliminate the x-term:
(20x + 15y) - (20x - 16y) = 140 - (-108)
20x + 15y - 20x + 16y = 140 + 108
31y = 248
Now, divide both sides of the equation by 31 to solve for y:
31y/31 = 248/31
y = 8
Substitute the value of y (y = 8) back into equation 1 to solve for x:
5x - 4y = -27
5x - 4(8) = -27
5x - 32 = -27
5x = 5
x = 1
Therefore, the solution to the system of equations is x = 1 and y = 8.
Original equations:
1) 5x - 4y = -27
2) 4x + 3y = 28
Multiply equation 1 by 4:
4(5x - 4y) = 4(-27)
20x - 16y = -108
Multiply equation 2 by 5:
5(4x + 3y) = 5(28)
20x + 15y = 140
New system:
3) 20x - 16y = -108
4) 20x + 15y = 140
Next, subtract equation 3 from equation 4 to eliminate the x-term:
(20x + 15y) - (20x - 16y) = 140 - (-108)
20x + 15y - 20x + 16y = 140 + 108
31y = 248
Now, divide both sides of the equation by 31 to solve for y:
31y/31 = 248/31
y = 8
Substitute the value of y (y = 8) back into equation 1 to solve for x:
5x - 4y = -27
5x - 4(8) = -27
5x - 32 = -27
5x = 5
x = 1
Therefore, the solution to the system of equations is x = 1 and y = 8.