PLEASE HELP!!!

$1.6x-0.9y=5.1$

$-0.4x+1.3y=4.1$

There are many ways to solve for x and y.  This is one of the ways.

Solve for x in the first equation

$1.6x-0.9y=5.1$

$1.6x=5.1+0.9y$

$x=\frac{5.1+0.9y}{1.6}$

Substitute x in the second equation and solve for y

$-0.4x+1.3y=4.1$

$-0.4\times\frac{5.1+0.9y}{1.6}+1.3y=4.1$

$\frac{5.1+0.9y}{1.6}+1.3y=-10.25$

$5.1+0.9y+1.3y=-16.4$

$0.9y+1.3y=-21.5$

$2.2y=-21.5$

$y≈-9.7727272727$

Replace y in the first equation and solve for x

$1.6x-0.9y=5.1$

$1.6x-0.9\times(-9.7727272727)≈5.1$

$1.6x-(-8.79545454543)≈5.1$

$1.6x+8.79545454543≈5.1$

$1.6x≈-3.69545454543$

$x≈-2.30965909089375$

$x≈-2.30965909089375 & y≈-9.7727272727$

Good try gibsonj, but you should check your working.  I get the following:

Start by multiplying all terms by 10 to get:

Solve the following system:
{1.3 y-0.4 x = 4.1
1.6 x-0.9 y = 5.1

In the first equation, look to solve for x:
{1.3 y-0.4 x = 4.1
1.6 x-0.9 y = 5.1

1.3 y-0.4 x = (13 y)/10-(2 x)/5 and 4.1 = 41/10:
(13 y)/10-(2 x)/5 = 41/10

Subtract (13 y)/10 from both sides:
{-(2 x)/5 = 1/10 (41-13 y)
1.6 x-0.9 y = 5.1

Multiply both sides by -5/2:
{x = 1/4 (13 y-41)
1.6 x-0.9 y = 5.1

Substitute x = 1/4 (13 y-41) into the second equation:
{x = 1/4 (13 y-41)
0.4 (13 y-41)-0.9 y = 5.1

0.4 (13 y-41)-0.9 y = (5.2 y-16.4)-0.9 y = 4.3 y-16.4:
{x = 1/4 (13 y-41)
4.3 y-16.4 = 5.1

In the second equation, look to solve for y:
{x = 1/4 (13 y-41)
4.3 y-16.4 = 5.1

4.3 y-16.4 = (43 y)/10-82/5 and 5.1 = 51/10:
(43 y)/10-82/5 = 51/10

Add 82/5 to both sides:
{x = 1/4 (13 y-41)
(43 y)/10 = 43/2

Multiply both sides by 10/43:
{x = 1/4 (13 y-41)
y = 5

Substitute y = 5 into the first equation:
Answer: |  x = 6        and            y=5