Solve the system: 2x+y=9 10x-4y=36

We have to solve for x and y using the system

2x + y = 9...(1)

10x - 4y = 36...(2)

Using (1)

2x + y = 9

=> y = 9 - 2x

substitute this in (2)

=> 10x - 4( 9 - 2x )  = 36

=> 10x - 36 + 8x = 36

=> 18x = 72

=> x = 4

y = 9 - 2*4 = 9 - 8 = 1

Therefore x = 4 and y = 1.

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This is a simple quadratic function.

To solve x or y, we need to put the coefficient of x or y same for each equation so that x or y can be eliminated when we subtract or add the two equations.

Let's eliminate y.

The coefficient of y in the first equation is 1, and in the second equation, it is -4. Therefore, if we multiply 4 to the first equation, the coefficients of ys in the both equation will be same.

4(2x +y=9)

==> 8x +4y= 36

Now, let's add both the equation.

8x+4y=36

+)10x-4y=36

18x       = 72

18x=72

x=72/18 = 4

Now, let's  solve y.

Substitute x for 4. Then, the first equation is

2(4) + y=9

8+y=9

y=1

Therefore, x=4, y=1.

Let's check if these two values are correct.

If we substitute these values in the second equation,

10(4) -4(1)=36

40-4=36

Since the equation is correct, x=4 and y=1.

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