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Use elimination to solve each system below.
System 1. 2x+5y=0 2x+3y=-8
System 2. 3x+2y=7 2x+y=4
Enter the values of x and y in the solution for each system in the following table.

Use elimination to solve each system below System 1 2x5y0 2x3y8 System 2 3x2y7 2xy4 Enter the values of x and y in the solution for each system in the following class=


Answer :

Answer:

x = - 10, y = 4 and x = 1, y = 2

Step-by-step explanation:

System 1

2x + 5y = 0 → (1)

2x + 3y = - 8 → (2)

subtract (2) from (1) term by term to eliminate x

(2x - 2x ) + (5y - 3y ) = 0 - (- 8)

0 + 2y = 0 + 8

2y = 8 ( divide both sides by 2 )

y = 4

substitute y = 4 into either of the 2 equations and solve for x

substituting into (1)

2x + 5(4) = 0

2x + 20 = 0 ( subtract 20 from both sides )

2x = - 20 ( divide both sides by 2 )

x = - 10

Solution to system 1 is x = - 10, y = 4

System 2

3x + 2y = 7 → (1)

2x + y = 4 → (2)

multiplying (2) by - 2 and adding the result to (1) will eliminate y

- 4x - 2y = - 8 → (3)

add (1) and (3) term by term to eliminate y

(3x - 4x ) + (2y - 2y ) = 7 - 8

- x + 0 = - 1

- x = - 1 ( multiply both sides by - 1 )

x = 1

substitute x = 1 into either of the 2 original equations and solve for y

substituting into (1)

3(1) + 2y = 7

3 + 2y = 7 ( subtract 3 from both sides )

2y = 4 ( divide both sides by 2 )

y = 2

Solution to system 2 is x = 1 , y = 2

Orelark
To answer your systems, the best way is to do them one at a time. Elimination in math is where you find a way to solve the equation for x and y. It doesn’t matter which variable you solve first.

System 1.

2x + 5y = 0 *****easiest way is to write the second equation below it.
2x + 3y = -8 *****it looks like the x’s will be the easiest to solve. To subtract
multiply the second line by -1. Could do to first line doesn’t matter.

2x + 5y = 0
(-1)(2x) + (-1)(3y) = (-1)(-8)
___________________ *now multiply bottom line and then add equations.
together.

2x + 5y = 0
+
-2x -3y = 8
___________
2y = 8 *divide both sides by 2, to make 2y equal to y

2y/2 = 8/2

y = 4

Don’t forget you now must solve for x. Easiest way is to use the other equation, so you can check your answer to y is right.

2x + 5y = 0

2x + 5(4) = 0

2x + 20 = 0

2x +20 -20 = 0 + (-20)

2x = -20

2x/2 = -20/2

x = -10

Now check your answers x = -10 and y = 4 with both equations

2(-10)+ 5(4) = -8

-20+ 20= 0


The answers for system 1 are x = -10 and y = 4




Question 2

3x + 2y = 7
2x + y = 4 *****if you multiply the bottom equation by -2 the y’s will drop off

3x +2y = 7
+
(-2)2x +(-2)(y) = (-2)(4)

3x +2y = 7
+
-4x - 2y = -8
____________
-x = -1 *****multiply both sides by -1 to make x positive

x = 1 *****substitute x = 1 into the first equation and solve for y

3x + 2y = 7

3(1) +2y = 7

3 + 2y = 7 *****subtract 3 from both sides of equal sign to isolate y

3 - 3 + 2y = 7 - 3

2y = 4 *****divide both sides by 2 to make it 1y or (y)

2y/2 =4/2

y = 2

x = 1 and y = 2

Substitute these numbers in for the variables.

2x + y = 4

2(1) + 2 = 4

2 + 2 = 4

4 = 4 *****these numbers work.

The answers for system 2 are: x = 1 and y = 2

I hope this helps you. Please let me know.







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