Question

Solve the system of equations

Answer 1

Solve the following system:
{1.8 x - 0.5 y = -6.4
{0.6 x + 2.1 y = 2.4

In the first equation, look to solve for x:
{1.8 x - 0.5 y = -6.4
{0.6 x + 2.1 y = 2.4

1.8 x - 0.5 y = (9 x)/5 - y/2 and -6.4 = -32/5:
{(9 x)/5 - y/2 = -32/5


Add y/2 to both sides:
{(9 x)/5 = 1/10 (5 y - 64)
{0.6 x + 2.1 y = 2.4

Multiply both sides by 5/9:
{x = 1/18 (5 y - 64)
{0.6 x + 2.1 y = 2.4

Substitute x = 1/18 (5 y - 64) into the second equation:
{x = 1/18 (5 y - 64)
{2.1 y + 0.0333333 (5 y - 64) = 2.4

2.1 y + 0.0333333 (5 y - 64) = 2.1 y + (0.166667 y - 2.13333) = 2.26667 y - 2.13333:
{x = 1/18 (5 y - 64)
2.26667 y - 2.13333 = 2.4

In the second equation, look to solve for y:
{x = 1/18 (5 y - 64)
{2.26667 y - 2.13333 = 2.4

2.26667 y - 2.13333 = (34 y)/15 - 32/15 and 2.4 = 12/5:
(34 y)/15 - 32/15 = 12/5

Add 32/15 to both sides:
{x = 1/18 (5 y - 64)
{(34 y)/15 = 68/15

Multiply both sides by 15/34:
{x = 1/18 (5 y - 64)
y = 2


Substitute y = 2 into the first equation:

Answer: {x = -3, y = 2