How do you solve the system using the elimination method for 2x+3y=7 and 3x+4y=10?

1 Answer
Aug 16, 2015

Answer:

#color(red)("The solution is (2,1).")#

Explanation:

Step 1. Enter the equations.

[1] #2x+3y=7#
[2] #3x+4y=10#

Step 2. Multiply each equation by a number to get the lowest common multiple for the coefficients of one variable.

Multiply Equation 1 by #3# and Equation 2 by #2#.

[3] #6x+9y =21#
[4] #6x+8y=20#

Step 3. Subtract Equation 4 from Equation 3.

[5] #y=1#

Step 4. Substitute Equation 5 in Equation 1.

#2x+3y=7#
#2x+3×1 =7#
#2x+3=7#
#2x=4#

#x=2#

Solution: The solution that satisfies both equations is #(2,1)#.

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

#2x+3y=7#
#2×2+3×1=7#
#4+3=7#
#7=7#

#3x+4y=10#
#3×2+4×1=10#
#6+4=10#
#10=10#

They check!

Our solution is correct.