152k views
4 votes
Solve the system of equations (-2x -3y = 12)(3x + 2y = 7)

User Npjc
by
6.8k points

1 Answer

4 votes

EXPLANATION

Given the system of equations

Isolate x for -2x -3y = 12

Add 3y to both sides:

-2x -3y +3y = 12 +3y

Simplify:

-2x = 12 + 3y

Divide both sides by -2

-2x/-2 = 12/-2 + 3y/-2

Simplify:

x = -12/2 + 3y/2

Substitute x = - (12+3y)/2

3(-(12+3y)/2)+2y = 7

Simplify:

(-36-5y)/2 = 7

Isolate y for (-36-5y)/2 = 7

Multiply both sides by 2:

2(-36-5y)/2 = 7*2

Simplify:

-36 -5y = 14

Add 36 to both sides:

-36 -5y + 36 = 14 + 36

Simplify:

-5y = 50

Divide both sides by -5:

-5y/-5 = 50/-5

Simplify:

y= - 10

For x = -(12+3y)/2

Substitute y= -10

x = -(12+3(-10))/2

-(12+3(-10))/2

Remove the parentheses:

= - (12-3*10)/2

Simplifying:

12 - 3* 10 = -18

= -(-18)/2

Apply the fraction rule: (-a)/b = -(a/b)

=-(-18/2)

Divide the numbers

= -(-9)

Apply rule -(-a)=a

=9

So, x=9

The solutions to the system of equations are x=9, y =-10

User Nienn
by
7.2k points
Welcome to QAmmunity.org, where you can ask questions and receive answers from other members of our community.