Question

Can you PLSS help me answer these question?

AND PLS GIVE A EASY + DETAILED STEP BY STEP ON HOW U GOT THE ANSWER BC IM SLOW LOL

1. 3x - 2y = 11
x + 2y=9

2. 3x + y= 9
2x+ y = 5

3. -x - 2y=4
3x + 2y=4

4. x + 3y= (-2)
3x + 4y= (-1)

Answer 1

See below for answers and explanations

Explanation:

Problem 1

`\displaystyle \left \{ {{3x-2y=11} \atop {x+2y=9}} \right.\\\\(3x-2y)+(x+2y)=11+9\\3x+x-2y+2y=20\\4x=20\\x=5\\\\x+2y=9\\5+2y=9\\2y=4\\y=2\\\\(5,2)`

Problem 2

`\displaystyle \left \{ {{3x+y=9} \atop {2x+y=5}} \right.\\\\(3x+y)-(2x+y)=9-5\\3x-2x+y-y=4\\x=4\\\\2x+y=5\\2(4)+y=5\\8+y=5\\y=-3\\\\(4,-3)`

Problem 3

`\displaystyle \left \{ {{-x-2y=4} \atop {3x+2y=4}} \right.\\\\(-x-2y)+(3x+2y)=4+4\\3x-x-2y+2y=8\\2x=8\\x=4\\\\-x-2y=4\\-4-2y=4\\-2y=8\\y=-4\\\\(4,-4)`

Problem 4

`\displaystyle \left \{ {{x+3y=-2} \atop {3x+4y=-1}} \right.\\ \\\\\left \{ {{3x+9y=-6} \atop {3x+4y=-1}} \right.\\\\(3x+9y)-(3x+4y)=-6-(-1)\\3x-3x+9y-4y=-6+1\\5y=-5\\y=-1\\\\x+3y=-2\\x+3(-1)=-2\\x-3=-2\\x=1\\\\(1,-1)`

Basically, the goal is to eliminate one variable from a system of equations to solve for the other variable. In the case of problem 4, we had to multiply an equation by a constant in order to eliminate that variable.