To solve the system of equations:
1. \( 3x + 2y = 2 \)
2. \( -2x + y = 8 \)
we can use the method of substitution or elimination. However, since I cannot access Desmos directly, I'll illustrate how you would solve it step-by-step.
### Method 1: Substitution
**Step 1:** Solve one of the equations for one variable.
Let's solve the second equation for \( y \):
\[
y = 2x + 8
\]
**Step 2:** Substitute \( y \) in the first equation:
Now substitute this expression for \( y \) in the first equation:
\[
3x + 2(2x + 8) = 2
\]
**Step 3:** Simplify and solve for \( x \):
\[
3x + 4x + 16 = 2
\]
\[
7x + 16 = 2
\]
\[
7x = 2 - 16
\]
\[
7x = -14
\]
\[
x = -2
\]
**Step 4:** Substitute \( x \) back to find \( y \):
Now plug \( x = -2 \) back into the expression for \( y \):
\[
y = 2(-2) + 8
\]
\[
y = -4 + 8
\]
\[
y = 4
\]
### Solution:
The solution to the system of equations is:
\[
(x, y) = (-2, 4)
\]
### Method 2: Elimination
Alternatively, you can also use elimination:
**Step 1:** Multiply the second equation by 2 to align coefficients of \( y \):
\[
-4x + 2y = 16
\]
Now we have:
1. \( 3x + 2y = 2 \)
2. \( -4x + 2y = 16 \)
**Step 2:** Subtract the first equation from the second:
\[
(-4x + 2y) - (3x + 2y) = 16 - 2
\]
\[
-7x = 14
\]
\[
x = -2
\]
**Step 3:** Substitute \( x \) back to find \( y \):
Substituting \( x = -2 \) in \( -2x + y = 8 \):
\[
-2(-2) + y = 8
\]
\[
4 + y = 8
\]
\[
y = 4
\]
### Conclusion:
Again, the solution is:
\[
(x, y) = (-2, 4)
\]
You can graph these equations on Desmos to visualize the intersection point at (-2, 4).