Question

Solve the system of equations using your Desmos calculator:

3x+2y=2

−2x+y=8

Answer 1

Sorry I wasn't telling you to use desmos sorry

Answer 2

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).

Answer 3

No problem at all! I'm here to help you solve the equations without needing any specific tool. If you have any other questions or if there's something specific you'd like assistance with regarding the system of equations, feel free to ask!