Q:

8x + 6y = 48 2x - 3y = -6Which statements are true about the solution to the system equation?1. The ordered pair that is the solution to the system lies in quadrant II2. The x-coordinate of the solution is 33. The y-coordinate of the solution is 34. The y-coordinate of the solution is 45. The ordered pair that is the solution to the system lies is quadrant I6. The x- coordinate of the solution is -3 Which ones are true???

Accepted Solution

A:
2. The x-coordinate of the solution is 3
4. The y-coordinate of the solution is 4
5. The ordered pair that is the solution to the system lies is quadrant I

Proof:

Solve the following system:
{8 x + 6 y = 48 | (equation 1)
{2 x - 3 y = -6 | (equation 2)

Subtract 1/4 Γ— (equation 1) from equation 2:
{8 x + 6 y = 48 | (equation 1)
{0 x - (9 y)/2 = -18 | (equation 2)

Divide equation 1 by 2:
{4 x + 3 y = 24 | (equation 1)
{0 x - (9 y)/2 = -18 | (equation 2)

Multiply equation 2 by -2/9:
{4 x + 3 y = 24 | (equation 1)
{0 x+y = 4 | (equation 2)

Subtract 3 Γ— (equation 2) from equation 1:
{4 x+0 y = 12 | (equation 1)
{0 x+y = 4 | (equation 2)

Divide equation 1 by 4:
{x+0 y = 3 | (equation 1)
{0 x+y = 4 | (equation 2)

Collect results:

Answer:Β  {x = 3, y = 4

Solve the following system:
{8 x + 6 y = 48 | (equation 1)
{2 x - 3 y = -6 | (equation 2)

Subtract 1/4 Γ— (equation 1) from equation 2:
{8 x + 6 y = 48 | (equation 1)
{0 x - (9 y)/2 = -18 | (equation 2)

Divide equation 1 by 2:
{4 x + 3 y = 24 | (equation 1)
{0 x - (9 y)/2 = -18 | (equation 2)

Multiply equation 2 by -2/9:
{4 x + 3 y = 24 | (equation 1)
{0 x+y = 4 | (equation 2)

Subtract 3 Γ— (equation 2) from equation 1:
{4 x+0 y = 12 | (equation 1)
{0 x+y = 4 | (equation 2)

Divide equation 1 by 4:
{x+0 y = 3 | (equation 1)
{0 x+y = 4 | (equation 2)

Collect results:

Answer:Β  {x = 3, y = 4