Solve by elimination
-4x+3y=-11
3x-2y=10

  (x, y) = (8, 7)

Step-by-step explanation:

We can eliminate the x-variable if we multiply the first equation by 3 (the coefficient of x in the second equation) and add the product of the second equation and 4 (where 4 is the opposite of the x-coefficient in the first equation). Doing this gives ...

  3(-4x +3y) +4(3x -2y)= 3(-11) +4(10)

  -12x +9y +12x -8y = -33 +40 . . . . . eliminate parentheses

  y = 7 . . . . . collect terms

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We can eliminate the y-variable if we multiply the first equation by 2 (the opposite of the y-coefficient in the second equation) and add the product of the second equation and 3 (the y-coefficient in the first equation). This gives ...

  2(-4x +3y) +3(3x -2y) = 2(-11) +3(10)

  -8x +6y +9x -6y = -22 +30 . . . . . eliminate parentheses

  x = 8 . . . . . . . collect terms

The solution is (x, y) = (8, 7).

Comment on this solution

Usually, we would substitute the found value of one of the variables into either equation and solve for the other variable.

Here, I showed finding both variable values by elimination. That is also a way the problem can be solved. I did that here to show that it doesn't matter which variable you choose to eliminate. In this case, where the coefficients are not multiples of each other, it is no less work to choose one variable over the other.

x = 8/17 and y = - 73/17

Step-by-step explanation:

4x + 3y = -11 (1)

3x - 2y = 10 (2)

To solve by elimination methods, we must make the coefficients of either x or y to be the same in both equation. In this case, let us make the coefficients of y to be the same in both equation. To do this, multiply equation (1) by 2 (i.e the coefficient of y in equation 2) and multiply equation(2) by 3(i.e the coefficient of y in equation 1). This is done as follows:

2 x (4x + 3y = -11) (1)

3 x (3x - 2y = 10) (2)

8x + 6y = - 22 (3)

9x - 6y = 30 (4)

Add both equations together

8x + 6y = - 22 (3)

+ 9x - 6y = 30 (4)

17x = 8

Divide both side by the coefficient of x i.e 17

x = 8/17

Now we substitute the value of x into any of the equation (ie 3 or 4). In this case we'll use equation 4

9x - 6y = 30 (4)

9(8/17) - 6y = 30

72/17 - 6y = 30

Multiply true by 17 to express in linear form:

72 - 102y = 510

Collect like terms

- 102y = 510 - 72

- 102y = 438

Divide both side by the coefficient of y i.e - 102

y = 438/ - 102

y = - 73/17

Therefore x = 8/17 and y = - 73/17

answer: 20

step-by-step explanation: