How do you solve the simultaneous equations #3x+7y=26# and #4x+5y=13#?

2 Answers
Jul 18, 2015

Answer:

I found:
#x=-3#
#y=5#

Explanation:

I would multiply the first equation by #-4# and the second by #3# and add together the two equatins (in columns):
#{-12x-28y=-104#
#{12x+15y=39#
#0-13y=-65#
So: #y=65/13=5#
Substitute back this value into the first equation:
#3x+7*5=26#
#3x=26-35=-9#
#x=-9/3=-3#

Jul 18, 2015

Answer:

#color(red)(x = -3, y = 5)# or #color(red)("(-3, 5)")#

Explanation:

One way is to use the method of elimination.

Step 1. Enter the equations.

Equation (1) #3x+7y = 26#
Equation (2) #4x+5y = 13#

Step 2. Prepare the equations.

Multiply every term in each equation by a number so that equal terms can be eliminated.

Multiply Equation (1) by #4# and Equation (2) by #3#.

Equation (3) #12x +28y = 104#
Equation (4) #12x +15y = 39#

Step 3. Subtract Equation (4) from Equation (3).

(3) #12x +28y = 104#
(4) #12x +15y = 39#
(5) #bar(color(white)(000000)13y = 65)#

#y = 65/13#

Equation (6) # y = 5#

Step 4. Substitute Equation (6) in Equation (2).

#4x+5y = 13#
#4x+5×5 =13#
#4x+25 = 13#
#4x = 13-25#
#4x=-12#
#x = -12/4#

#x = -3#

Solution: #x = -3, y = 5# or #(-3, 5)#

Check: Substitute the values of #x# and #y# in Equation (1).

#3x+7y = 3(-3) + 7×5 = -9+35= 26#