Solve by elimination

5x+y=2
3x+y=1

This is what I got :
3(5x+y=2)
-5(3x+y=1)
15x+3y=6
-15x-5y=-5

-2y=1
2 2
Y=1/2

15x+3(1/2)=6
15x+3/2 =6
15x/15= 9/2 /15
X=3/10

If -2y = 1, then y = -1/2

Thus 3x + (-1/2) = 1, then:

3x = 3/2

x = 1/2

To solve the system of equations using the method of elimination, follow these steps:

Step 1: Write down both equations:
5x + y = 2 ...(Equation 1)
3x + y = 1 ...(Equation 2)

Step 2: Multiply Equation 2 by -1, so that the coefficients of y will cancel out when we add the two equations together:
-1(3x + y) = -1(1)
-3x - y = -1 ...(Equation 3)

Step 3: Add Equation 1 and Equation 3:
(5x + y) + (-3x - y) = 2 + (-1)
2x = 1

Step 4: Divide both sides of the equation by 2 to isolate x:
2x/2 = 1/2
x = 1/2

Step 5: Substitute the value of x into Equation 1 and solve for y:
5(1/2) + y = 2
5/2 + y = 2
y = 2 - 5/2
y = 4/2 - 5/2
y = -1/2

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