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Solve this system of equations using the elimination method.
3x - 2y = 0
2x+y = 7
The solution to the system is
I
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Answer 1

Hi,

x=2 and y=3

Explanation:

To solve this system of equations using the elimination method, we can multiply one or both of the equations by a suitable factor to make the coefficients of either x or y in one of the equations match. In this case, it's convenient to eliminate the y variable. Here's the system of equations:

3x - 2y = 0

2x + y = 7

First, let's make the coefficients of y in both equations equal. To do this, multiply the second equation by 2, which will make the coefficients of y equal:

3x - 2y = 0

4x + 2y = 14

Now, we can add the two equations together to eliminate the y variable:

(3x - 2y) + (4x + 2y) = 0 + 14

Combine like terms:

3x + 4x = 14

7x = 14

Now, divide both sides by 7 to solve for x:

7x/7 = 14/7

x = 2

Now that we have found the value of x, we can substitute it back into one of the original equations to find the value of y. Let's use the second equation:

2x + y = 7

2(2) + y = 7

4 + y = 7

Subtract 4 from both sides:

y = 7 - 4

y = 3

So, the solution to the system of equations is:

x = 2

y = 3

`\left\{\begin{array}c3x-2y&=&0&1&2\\2x+y&=&7&2&-3\\\end {array}\right.\\\\\\\left\{\begin{array}{ccc}7x&=&14\\-7y&=&-21\\\end {array}\right.\\\\\\\left\{\begin{array}{ccc}x&=&2\\y&=&3\\\end {array}\right.\\\\\\`