Question

3x + y = 3
x + y = 2

Solve the system of equations.
Responses
A x = 12
, y = 3x = 1 2 , y = 3
B x = 3, y = 12
x = 3, y = 1 2
C x = 12
, y = 32
x = 1 2 , y = 3 2
D x = 32
, y = 12
x = 3 2 , y = 1 2
E x = 52
, y = -92

Answer 1

To solve this system of equations, we can use the method of substitution or the method of elimination. Let's use the method of substitution.

From the second equation, we know that x + y = 2. Rearrange this equation to solve for y: y = 2 - x.

Substitute this expression for y in the first equation: 3x + (2 - x) = 3.

Simplify the equation: 3x + 2 - x = 3.

Combine like terms: 2x + 2 = 3.

Subtract 2 from both sides: 2x = 1.

Divide both sides by 2: x = 1/2.

Now substitute this value for x in the second equation: (1/2) + y = 2.

Subtract 1/2 from both sides: y = 2 - 1/2.

Simplify the equation: y = 3/2.

Therefore, the solution to the system of equations is x = 1/2 and y = 3/2.

This matches with option C: x = 1/2 and y = 3/2.