Question

8x-21y=50 6x+17y=-28

Answer 1

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Answer 2

To solve this system of linear equations:

1. Multiply both sides of the first equation by 3 and the second equation by 2 to make it easier to eliminate one of the variables when you add or subtract the equations. This will help you eliminate one of the variables:

   Equation 1: 3(8x - 21y) = 3(50) => 24x - 63y = 150 Equation 2: 2(6x + 17y) = 2(-28) => 12x + 34y = -56

2. Now, you can either add or subtract the two equations to eliminate one of the variables. Let's subtract the second equation from the first:

   (24x - 63y) - (12x + 34y) = 150 - (-56)

   Simplify:

   24x - 63y - 12x - 34y = 150 + 56

   12x - 97y = 206

3. Now, you have a new equation with only one variable (x):

   12x - 97y = 206

4. You can solve for x:

   12x = 206 + 97y

   Divide both sides by 12:

   x = (206 + 97y) / 12

5. Now, you can substitute this expression for x into one of the original equations to solve for y. Let's use the second equation:

   6x + 17y = -28

   6[(206 + 97y) / 12] + 17y = -28

   Simplify:

   (1030 + 582y) / 12 + 17y = -28

6. Multiply both sides of the equation by 12 to get rid of the fraction:

   1030 + 582y + 204y = -336

7. Combine like terms:

   786y + 1030 = -336

8. Subtract 1030 from both sides:

   786y = -336 - 1030

   786y = -1366

9. Divide by 786 to solve for y:

   y = -1366 / 786

   y = -683 / 393

10. Now that you have the value of y, you can substitute it back into one of the original equations to solve for x. Let's use the first equation:

8x - 21y = 50

8x - 21(-683/393) = 50

8x + (21 * 683/393) = 50

8x + 14223/393 = 50

11. Subtract (14223/393) from both sides:

8x = 50 - 14223/393

12. Now, divide by 8 to solve for x:

x = (50 - 14223/393) / 8

x ≈ -0.943

So, the solution to the system of equations is approximately:

x ≈ -0.943 y ≈ -683/393