To solve the system of equations:
- \( 3x + 2y = 2 \)
- \( -2x + y = 8 \)
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:
- \( 3x + 2y = 2 \)
- \( -4x + 2y = 16 \)
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).