Solve the System: Find x and y in -5x + y = 8 and 3x - 2y = 11 Using Substitution

To solve this system of equations using the substitution method, we follow these steps:

• Step 1: Solve for one of the variables in terms of the other using the first equation $-5x + y = 8$.
• We solve for $y$:

$y = 5x + 8$

• Step 2: Substitute the expression for $y$ from Step 1 into the second equation $3x - 2y = 11$.

$3x - 2(5x + 8) = 11$

• Step 3: Simplify and solve for $x$.

Simplify the substitution:

$3x - 10x - 16 = 11$

$-7x - 16 = 11$

Add 16 to both sides:

$-7x = 27$

Divide by -7:

$x = -\frac{27}{7}$

• Step 4: Substitute $x$ back into the expression for $y$ from Step 1.

$y = 5\left(-\frac{27}{7}\right) + 8$

Simplify:

$y = -\frac{135}{7} + \frac{56}{7}$

$y = -\frac{135}{7} + \frac{56}{7} = -\frac{79}{7}$

Therefore, the solution to the system is $x = -\frac{27}{7}$ and $y = -\frac{79}{7}$.