What is the solution to the following system of equations? Write your answer as an ordered pair, i. e. (7,8): 2x+4y=6

8x+4y=0

Skip to content# What is the solution to the following system of equations? Write your answer as an ordered pair, i. e. (7,8):2x+4y=68x+4y=0

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8x+4y=0

(x, y ) = (3, 6 )

Step-by-step explanation:

given the 2 equations

2x - y = 0 → (1)

3x - 2y = - 3 → (2)

rearrange (2) to give y in terms of x

add y to both sides

y = 2x → (3)

Substitute y = 2x into (2)

3x - 2(2x) = - 3

3x - 4x = - 3

- x = - 3 ⇒ x = 3

substitute x = 3 into (3)

y = 2 × 3 = 6

Solution is (3, 6)

The system of equations you want to be solved is not given. I would however give an example with which the method of elimination will be shown, and can be used in solving problems of the nature.

Step-by-step explanation:

Consider the system of equations:

x + y = 7 (1)

2x - y = 8 (2)

To eliminate x:

First multiply (1) by 2 to have

2x + 2y = 14 (3)

Next, subtract (2) from (3) to have

3y = 6

y = 6/3 = 2

To eliminate y:

Add (1) and (2) to have

3x = 15

x = 15/3 = 5

Therefore, (x, y) = (5, 2).

Part I : Eliminating x terms

Step 1: There are two equations. To eliminate the x terms we have to make similar x-terms in both the equation.

Step 2: Cancel x- terms by using addition or subtraction of 2 equations.

Step 3: Find the value of y and substitute into any equation and find the value of y

Part II : Eliminating y terms

Step 1: There are two equations. To eliminate the y terms we have to make similar y-terms in both the equation.

Step 2: Cancel y- terms by using addition or subtraction of 2 equations.

Step 3: Find the value of x and substitute into any equation and find the value of x

The value of (x,y) = (-4.5, -10)

Step-by-step explanation:

It is given that,

2x-3y=21 (1)

-6x+2y=7 (2)

To find the value of x and y

Eliminating x terms:-

(1) ⇒ 2x-3y = 21

(1) * 3 ⇒ 6x - 9y = 63 (3)

Adding eq(2) and eq(3)

-6x + 2y = 7 (2)

6x - 9y = 63 (3)

-7y = 70

y = 70/-7 = -10

Substituting the value of y in eq(1)

eq(1) ⇒2x - 3y = 21

2x - 3 *(-10) = 21

2x + 30 = 21

2x = 21 - 30 = -9

x = -9/2 = -4.5

Therefore the value of (x,y) = (-4.5, -10)

31//4

Step-by-step explanation:

-2x + 6y = 6

6y - 6 = 2x

6(y-1) = 2x

(1/2) * 6(y-1) = 2x * (1/2)

x = 3(y-1)

If, x = 3(y-1),

-7 * 3(y-1) + 8y = -5

-21 * (y-1) + 8y = -5

-21y + 21 + 8y = -5

21 + 5 = 21y - 8y

26 = 13y

y = 26/13

Therefore: y=2.

If y=2,

x = 3(2-1) = 3

Answers:

x=3 and y=2.

(3, 1)

Step-by-step explanation:

To find when f(x) = g(x), you first have to set them equal to each other.

x - 2 = -2x + 7

Step 1. Add 2 to both sides

x = -2x + 9

Step 2. Add 2x to both sides.

3x = 9.

Step 3. Divide it all by 3 to isolate the variable.

x = 3

Now we just have to plug that 3 as X into both of the equations. I am changing f(x) and g(x) into y so it is easier to understand for most.

For f(x): y = 3 - 2. y = 1.

For g(x): y = -2(3) + 7. y = -6 + 7. y = 1.

[tex]If f(x) = x – 2 and g(x) = –2x + 7, what value of x makes f(x) = g(x)? use the substitution method[/tex]

(3, 1)

Step-by-step explanation:

x = y + 2

y = -2x + 7

y = -2(y +2) +7

y = -2y -4 +7

y + 2y = 3

3y = 3

y = 3/3

y = 1

x = y +2

x = 1 +2

x = 3

(-3, -2)

Step-by-step explanation:

Look at the second equation, we can easily rearrange it to make x the subject.

x - 4y = 5

x = 4y + 5

Now lets put that into the second equation

2x - 2y = -2

2(4y + 5) - 2y = -2

6y + 10 = -2

6y = -12

y = -2

Now lets find x!

x = 4y + 5

x = 4(-2) + 5

x = -3

Now lets format the answer like the question says (ordered pair)

(-3, -2)

Recap: We used substitution and made an equation to work out one of the variables first, then found the second variable using the first.

2x - 2y = -2

x - 4y = 5

In x -4y =5, add 4y to both sides to get x = 4y +5

Now substitute that equation for x in the first equation:

2x - 2y = -2

2(4y +5) - 2y = -2

Simplify:

8y +10 - 2y = -2

Combine like terms:

6y +10 = -2

Subtract 10 from both sides:

6y = -12

Divide both sides by 6:

y = -12 /6

y = -2

Now you have y, substitute y in the second equation to solve for x:

x - 4y = 5

x -4(-2) = 5

Simplify:

x+8 = 5

Subtract 8 from both sides:

x = -3

Now you have x = -3 and y = -2

The answer is (-3,-2)

Step-by-step explanation:

Hello!

[tex]f(x)=g(x)=\\x-2=-2x+7\\-2=-3x+7\\-3x=-9=x=3\\y=x-2=3-2=1\\y=-2x+7=-6+7=1\\[/tex]

Good luck!