To find the solution set of the system:
1. Rewrite the system of equations:
X - 2y = 10 ...(1)
2x + 3y = 8 ...(2)
2. Multiply equation (1) by 2 to eliminate the variable x:
2(X - 2y) = 2(10)
2x - 4y = 20 ...(3)
3. Add equations (2) and (3) together to eliminate the variable x:
(2x + 3y) + (2x - 4y) = 8 + 20
4x - y = 28 ...(4)
4. Solve equation (4) for y:
y = 4x - 28 ...(5)
5. Substitute the value of y from equation (5) into equation (1):
X - 2(4x - 28) = 10
X - 8x + 56 = 10
-7x + X = -46
-6x = -46
x = -46 / -6
x = 23/3
6. Substitute the value of x back into equation (5) to find y:
y = 4(23/3) - 28
y = 92/3 - 84/3
y = 8/3
Therefore, the solution set of the system is:
x = 23/3
y = 8/3
19. What is the solution set of the system
X-2y =10
2x + 3y =8
1 answer