How do you solve the following system?: # 2x+y=3 , 2y=5x-3 #

Question

How do you solve the following system?: # 2x+y=3   ,  2y=5x-3  #

Eva Adamson · Accepted Answer

The solution for the system of equations is:
#color(blue)(x=1#
#color(blue)(y=1# #2x +y=3#, multiplying by #2# #4x +color(blue)(2y)=6#.......equation #(1)# #5x-color(blue)(2y)=3#........equation #(2)# Using elimination to solve Adding equations #(2)# and #(1 )# results in elimination of #color(blue)(2y# #4x +cancelcolor(blue)(2y)=6# #5x-cancelcolor(blue)(2y)=3# #9x=9# #x=9/9# #color(blue)(x=1# Finding #y# from equation #1#: #2x +y=3# # y=3 - 2x# # y=3 - 2 xx 1# # y=3 - 2# #color(blue)(y=1#

Isaiah Anthony · Answer

undefined To solve the system of equations 2x + y = 3 and 2y = 5x - 3, you can use either the substitution method or the elimination method. Let's use the elimination method:

Step 1: Rearrange the equations to put them in standard form:
- Equation 1: 2x + y = 3
- Equation 2: 5x - 2y = 3

Step 2: Multiply both sides of Equation 1 by 2 to make the coefficients of y the same in both equations:
- Equation 1 (after multiplication): 4x + 2y = 6

Step 3: Add Equation 2 to the modified Equation 1 to eliminate y:
- 5x - 2y + 4x + 2y = 3 + 6
- Simplify and solve for x:
- 9x = 9
- x = 1

Step 4: Substitute the value of x into either Equation 1 or Equation 2 to solve for y. Let's use Equation 1:
- 2(1) + y = 3
- 2 + y = 3
- y = 3 - 2
- y = 1

Step 5: Check the solution by substituting the values of x and y into both equations:
- For Equation 1: 2(1) + 1 = 3 (True)
- For Equation 2: 2(1) = 5(1) - 3 => 2 = 5 - 3 (True)

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