{2x + y = 2
{5x + 3y - 9
Solution: We can solve this system of equations either by substitution or elimination method. Here, let's use substitution method.
From equation 1, we have: y = -2x + 2
Substituting this in equation 2, we get: 5x + 3(-2x + 2) - 9 = 0
Expanding the right-hand side, we get: 5x - 6x + 6 - 9 = 0
Simplifying further, we get: -x + (-3) = 0
Adding x to both sides, we get: -3 = x
Substituting this value of x in y = -2x + 2, we get: y = -2(-3) + 2 = 6
So, the solution to the system of equations is (x, y) = (-3, 6)
{5x - 2y = -2
{3x + 4y - 30
Solution: We can solve this system of equations by either substitution or elimination method. Here, let's use elimination method.
We can multiply equation 1 by 3 and equation 2 by 2, to make the coefficients of y same in both equations. Doing this, we get:
15x - 6y = -6
6x + 8y - 60 = 0
Adding these two equations, we get: 21x + 2y - 60 = 0
Simplifying further, we get: 21x = 60 + 2y
Dividing both sides by 21, we get: x = (60 + 2y)/21
Substituting this in equation 1, we get: 5((60 + 2y)/21) - 2y = -2
Expanding the right-hand side, we get: 60/21 + 10/21 y - 2y = -2
Simplifying further, we get: 60/21 + (-12/21) y = -2
Adding 12/21 y to both sides, we get: 60/21 = (-2) + (12/21) y
Subtracting -2 from both sides, we get: 62/21 = (12/21) y
Dividing both sides by 12/21, we get: y = 62/12 = 5 1/6
Substituting this value of y in x = (60 + 2y)/21, we get: x = (60 + 2(5 1/6))/21 = (60 + 11 1/3)/21 = (71 1/3)/21 = 71/21 + 1/63
So, the solution to the system of equations is (x, y) = (71/21 + 1/63, 5 1/6)