How do you solve #3x + 7y = -6# and #x - 2y = 11#?

1 Answer
Aug 15, 2015

Answer:

#color(red)("The solution is (5,-3).")#

Explanation:

One way is to use the method of elimination.

Step 1. Enter the equations.

[1] #3x+7y=-6#
[2] #x-2y=11#

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

Multiply Equation 2 by #3#.

[3] #3x-6y =33#

Step 3. Subtract Equation 3 from Equation 1.

#3x+7y=-6#
#3x-6y =33#
#stackrel(——————————)(" "color(white)(1)13y=-39)#

[4] #y = -3#

Step 4. Substitute Equation 4 in Equation 1.

#3x+7y=-6#
#3x+7(-3)= -6#
#3x-21=-6#
#3x=15#

#x=5#

Solution: The solution that satisfies both equations is #(5,-3)#.

Check: Substitute the values of #x# and #y# in Equation 2.

#x-2y=11#
#5-2(-3) =11#
#5+6=11#
#11=11#

It checks!

Our solution is correct.