Question

What is the solution of the system?

Use the elimination method.

4x + 2y = 18
2x + 3y = 15

Enter the answer in the boxes.

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Answer 1

To solve this system of equations using the elimination method, we multiply one or both equations so that the coefficients of either x or y are the same or additive inverses. Then, we subtract one equation from the other to eliminate one variable. Finally, we solve for the remaining variable by substituting the value of the other variable.

Step-by-step explanation:

To solve the system of equations using the elimination method, we need to eliminate one variable by multiplying one or both equations so that the coefficients of either x or y are the same or additive inverses. In this case, we can multiply the first equation by 3 and the second equation by 2:

12x + 6y = 54

4x + 6y = 30

Next, we subtract the second equation from the first:

(12x + 6y) - (4x + 6y) = 54 - 30

8x = 24

Divide both sides by 8 to solve for x:

x = 3

To find the value of y, substitute the value of x into either of the original equations:

4(3) + 2y = 18

12 + 2y = 18

2y = 18 - 12

2y = 6

y = 6/2

y = 3

Answer 2

Greetings!

Solve the System, using Elimination:

`\left \{ {{4x+2y=18} \atop {2x+3y=15}} \right.`

Multiply Equation #2 by 2:

`\left \{ {{4x+2y=18} \atop {2(2x+3y)=2(15)}} \right.`


`\left \{ {{4x+2y=18} \atop {4x+6y=30}} \right.`

Eliminate variable x:

`-\frac{ \left \{ {{4x+2y=18} \atop {4x+6y=30}} \right.}{0x-4y=-12}`


`4y=-12`

Divide both sides by 4:

`(4y)/(4)= (12)/(4)`


`y=3`

Input this value into one of the Equations:

`4x+2y=18`


`4x+2(3)=18`

Simplify:

`4x+6=18`


`(4x+6)+(-6)=(18)+(-6)`


`4x=12`

Divide both sides by 4.

`(4x)/(4)= (12)/(4)`


`x=3`

The Solution to this System (The Point of Intersection):

`\boxed{(3,3)}`

I hope this helped!
-Benjamin