To solve the system of equations by substitution, we have the following equations:
- \(-5x + 3y = 2\) (Equation 1)
- \(y = 2x\) (Equation 2)
Step 1: Substitute Equation 2 into Equation 1
We can substitute \(y\) from Equation 2 into Equation 1:
\[ -5x + 3(2x) = 2 \]
Step 2: Simplify the equation
Now, simplify the equation:
\[ -5x + 6x = 2 \]
This simplifies to:
\[ x = 2 \]
Step 3: Solve for \(y\)
Now that we have \(x\), we can use Equation 2 to find \(y\):
\[ y = 2x = 2(2) = 4 \]
Final Solution
The solution to the system of equations is:
\[ x = 2, \quad y = 4 \]
In coordinate form, the solution is \((2, 4)\).