How do you solve the simultaneous equations #4x + 3y = 9# and #3x - y = 10#?

1 Answer
Aug 3, 2015

Answer:

#color(red)( x=3,y=-1)#

Explanation:

One way is to use the method of elimination.

Step 1. Enter the equations.

[1] #4x+3y=9#
[2] #3x-y=10#

Step 2. Prepare the equations.

Multiply each equation by numbers that give one variable the same coefficient in each equation.

Multiply Equation 2 by #3#.

[3] #9x-3y=30#

Step 2. Add Equations 1 and 3.

#13x=39#

[3] #x=3#

Step 3. Substitute Equation 3 in Equation 2.

#3x-y=10#
#3(3)-y=10#
#9-y=10#

#y=-1#

Solution: #x=3,y=-1#

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

#4x+3y=9 #
#4(3) +3(-1)=9#
#12-3=9#
#9=9#

It checks!