How do you solve #3x – 2y = 26# and #-7x + 3y = -49# using substitution?

Question

Hazel Anglin · Accepted Answer

#x = 4#
#y =-7# Solve by simultaneous equations: #3x - 2y = 26# #-7x+3y = -49# Rearrange #3x - 2y = 26# to make #x# the subject of the equation: #3x = 26 + 2y# #x = (26 + 2y) / 3# Substitute the value of #x# into #-7x+3y = -49#: #-7*((26 + 2y) / 3) + 3y = -49# #-7*(26/3 + (2y)/3) + 3y = -49# Multiply out the brackets: #-182/3 + -(14y)/3 + 3y = -49# Rearrange and place like terms together: #-(14y)/3 + 3y = -49 + 182/3# Simplify and solve for y: #-(5y)/3 = 35/3# #-5y = 35/3 *3# #-5y = 35# #y = 35 / -5# #y = -7# Use value of y to subsitute into any of the two original equations and solve for x: #3x - 2y = 26# #3x - 2*(-7) = 26# #3x + 14 = 26# #3x = 26 - 14# #3x = 12# #x = 12/3# #x = 4#

Nathan Axel · Answer

undefined To solve the system of equations using substitution, follow these steps:

1. Solve one of the equations for one variable.
2. Substitute the expression obtained in step 1 into the other equation.
3. Solve the resulting equation for the remaining variable.
4. Substitute the value found in step 3 back into one of the original equations to solve for the other variable.
5. Check the solution by substituting the values of both variables into both original equations.

Let's solve the system of equations:

1. From the first equation, solve for x:
   3x - 2y = 26
   => 3x = 26 + 2y
   => x = (26 + 2y) / 3

2. Substitute the expression for x into the second equation:
   -7x + 3y = -49
   => -7((26 + 2y) / 3) + 3y = -49

3. Solve for y:
   -7((26 + 2y) / 3) + 3y = -49
   => -7(26 + 2y) + 9y = -147
   => -182 - 14y + 9y = -147
   => -5y = 35
   => y = -7

4. Substitute y = -7 into one of the original equations. Let's use the first equation:
   3x - 2(-7) = 26
   => 3x + 14 = 26
   => 3x = 26 - 14
   => 3x = 12
   => x = 4

5. Check the solution by substituting x = 4 and y = -7 into both original equations:
   For the first equation: 3(4) - 2(-7) = 26
                           12 + 14 = 26 (True)
   For the second equation: -7(4) + 3(-7) = -49
                            -28 - 21 = -49 (True)

Therefore, the solution to the system of equations using substitution method is x = 4 and y = -7.