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
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.
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.
