Graph the system of equations. $$ 3 x+5 y=10 $$ $$ x-5 y=-10 $$

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Rewrite the equation by following steps:
- step0: Rewrite in slope-intercept form:
  $$3x+5y=10$$
- step1: Move the expression to the right side:
  $$5y=10-3x$$
- step2: Divide both sides:
  $$y=2-\frac{3}{5}x$$
- step3: Rearrange the terms:
  $$y=-\frac{3}{5}x+2$$
Rewrite the equation $$ x - 5 y = -10 $$.
Rewrite the equation by following steps:
- step0: Rewrite in slope-intercept form:
  $$x-5y=-10$$
- step1: Move the expression to the right side:
  $$-5y=-10-x$$
- step2: Divide both sides:
  $$y=2+\frac{1}{5}x$$
- step3: Rearrange the terms:
  $$y=\frac{1}{5}x+2$$
To graph the system of equations, we first convert both equations into slope-intercept form $$y = mx + b$$.

1. **First Equation:**
   $$
   3x + 5y = 10
   $$
   Rearranging gives:
   $$
   5y = -3x + 10 \implies y = -\frac{3}{5}x + 2
   $$

2. **Second Equation:**
   $$
   x - 5y = -10
   $$
   Rearranging gives:
   $$
   -5y = -x - 10 \implies y = \frac{1}{5}x + 2
   $$

Now we have the two equations in slope-intercept form:
- $$y = -\frac{3}{5}x + 2$$
- $$y = \frac{1}{5}x + 2$$

### Graphing the Equations
- The first equation has a slope of $$-\frac{3}{5}$$ and a y-intercept of $$2$$.
- The second equation has a slope of $$\frac{1}{5}$$ and also a y-intercept of $$2$$.

Both lines intersect at the point where $$y = 2$$.

To visualize the graph, you can plot these two lines on a coordinate plane. The intersection point can be found by setting the equations equal to each other:

$$
-\frac{3}{5}x + 2 = \frac{1}{5}x + 2
$$

This will help you find the exact point of intersection if needed. However, since both lines have the same y-intercept, they will intersect at $$x = 0$$ and $$y = 2$$.

If you need a graphical representation, you can use graphing software or tools to plot these equations.
To graph the system of equations: 1. Convert both equations to slope-intercept form: - $$ y = -\frac{3}{5}x + 2 $$ - $$ y = \frac{1}{5}x + 2 $$ 2. Plot both lines on a coordinate plane. 3. The lines intersect at $$ (0, 2) $$.

Graph the system of equations. \( 3 x+5 y=10 \) \( x-5 y=-10 \)

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