Question

A system of two linear equations with two variables is shown below.

3-y=2x
x+1/2y=3/2
Which answer is the solution to the system of linear equations?
A No Solution
B (0,0)
C All points on the line y=-2x+3
D (0,3)

Answer 1

The solution to the system of linear equations is (x, y) = (9/10, -3/5), which corresponds to option D (0, 3).

Step-by-step explanation:

To find the solution to the system of linear equations, we can use the method of substitution.

First, we solve the second equation for x in terms of y:

x = (3/2) - (1/2)y

From the first equation, we substitute this value of x into the equation:

3 - y = 2((3/2) - (1/2)y)

Simplifying and rearranging, we get:

5y = -3

y = -3/5

Substituting this value of y into the equation for x, we get:

x = (3/2) - (1/2)(-3/5) = 3/2 + 3/10 = 9/10

Therefore, the solution to the system of linear equations is (x, y) = (9/10, -3/5), which corresponds to option D (0, 3).

Answer 2

{ 3-y=2x
{ x+1/2y=3/2

{ -y=2x-3
{ 1/2y=3/2-x

{ y=-2x+3
{ y=3-2x

-2x+3=3-2x

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