What is the solution to -2x+5y=-1 and 3x+2y=11 by using elimination method
-2x + 5y = -1
3x + 2y = 11
-6x + 15y = -3
6x + 4y = 22
19y = 19
y=1
so,
x=3
To solve the system of equations -2x + 5y = -1 and 3x + 2y = 11 using the elimination method, follow these steps:
Step 1: Multiply the first equation by 3 and the second equation by 2 to make the coefficients of x in both equations the same.
Original equations:
-2x + 5y = -1
3x + 2y = 11
Multiply the first equation by 3:
(3)(-2x + 5y) = (3)(-1)
-6x + 15y = -3
Multiply the second equation by 2:
(2)(3x + 2y) = (2)(11)
6x + 4y = 22
The equations become:
-6x + 15y = -3
6x + 4y = 22
Step 2: Add the two equations together to eliminate the x variable.
(-6x + 15y) + (6x + 4y) = (-3) + (22)
-6x + 6x + 15y + 4y = 19
19y = 19
Simplify and solve for y:
19y = 19
y = 19/19
y = 1
Step 3: Substitute the value of y back into one of the original equations to solve for x. Let's use the first equation:
-2x + 5(1) = -1
-2x + 5 = -1
-2x = -1 - 5
-2x = -6
x = -6/(-2)
x = 3
Step 4: Write the solution as an ordered pair (x, y):
The solution to the system of equations -2x + 5y = -1 and 3x + 2y = 11 is (3, 1).