Question

Solve for y in the system of equations:
y+2x=5
3x-5y=9

Answer 1

To solve for y in the system of equations y + 2x = 5 and 3x - 5y = 9, you can use substitution. First solve one equation for y, substitute that expression into the other equation, and solve for x. Then, substitute the value of x back into the first equation to find y. The solution is approximately x = 2.6154 and y = -0.2308.

Step-by-step explanation:

To solve for y in the system of equations:

• Equation 1: y + 2x = 5
• Equation 2: 3x - 5y = 9

We can use the substitution or elimination method. Let's use the substitution method in this case:

1. Rearrange Equation 1 to solve for y:
   y = 5 - 2x.
2. Substitute this expression for y into Equation 2:
   3x - 5(5 - 2x) = 9.
3. Simplify and solve for x:
   3x - 25 + 10x = 9
   13x = 34
   x = 34/13
   x = 2.6154 (approx).
4. Substitute x back into the rearranged Equation 1 to find y:
   y = 5 - 2(2.6154)
   y = 5 - 5.2308
   y = -0.2308 (approx).

Therefore, the solution to the system of equations is approximately x = 2.6154 and y = -0.2308.