Question

Solve for x and y in the system of equations:

y = (2/3)x - 2
y = -x + 3
a) x = 3, y = 1
b) x = 2, y = 4
c) x = 1, y = 2
d) x = 0, y = 3

Answer 1

To solve the provided system of equations, we set the two expressions for y equal, which gives us the solution x = 3 and y = 1.

Step-by-step explanation:

To solve for x and y in the system of equations provided, we set the two equations for y equal to each other since they must intersect at the solution point.

y = (2/3)x - 2
y = -x + 3

We equate the right-hand expressions:
(2/3)x - 2 = -x + 3

Next, we find a common denominator to combine x terms and solve for x:
2x - 6 = -3x + 9

Combining like terms,
5x = 15

Divide by 5,
x = 3

Substitute x back into one of the equations to solve for y:
y = (2/3)(3) - 2
y = 1

Therefore, the solution to the system is x = 3 and y = 1.