Solve Simultaneous Equetion Using Elimination Method: (A)2x - 3y= -3 and
3x - 7y= -1.
To solve this system of simultaneous equations using the elimination method, you need to eliminate one of the variables by adding or subtracting the two equations. Here's how you can do it:
Step 1: Multiply the first equation by 3 and the second equation by 2 to make the coefficients of x equal.
(A) 2x - 3y = -3
(B) 3x - 7y = -1
Multiply equation (A) by 3:
3 * (2x - 3y) = 3 * (-3)
6x - 9y = -9
Multiply equation (B) by 2:
2 * (3x - 7y) = 2 * (-1)
6x - 14y = -2
Step 2: Now, you can subtract equation (2) from equation (1) to eliminate x.
(6x - 9y) - (6x - 14y) = -9 - (-2)
6x - 9y - 6x + 14y = -9 + 2
-9y = -7
Step 3: Finally, solve for y by dividing both sides of the equation by -9:
-9y / -9 = -7 / -9
y = 7/9
Step 4: Substitute the value of y back into one of the original equations (A) or (B) to solve for x. Let's use equation (A):
2x - 3(7/9) = -3
2x - 21/9 = -3
2x - 7/3 = -3
Step 5: Solve for x by isolating it:
2x = -3 + 7/3
2x = -9/3 + 7/3
2x = -2/3
x = -1/3
So, the solution to the simultaneous equations is x = -1/3 and y = 7/9.
multiply the rows by 3 and 2 and you have
6x-9y = -9
6x-14y = -2
Now subtract to eliminate x, and then y is easy. Use that value of y in either equation to get x.