We are tasked with solving the system of linear equations:

1. $8x - 6y = -20$
2. $-16x + 7y = 30$.

Step 1: Simplify the system if possible

Equation (1):
$8x - 6y = -20$
Equation (2):
$-16x + 7y = 30$

There is no immediate simplification possible, so we proceed to solve the system.

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Step 2: Solve using substitution or elimination

We'll use elimination for this problem.

Eliminate $x$:

To eliminate $x$, we can multiply equation (1) by 2 to align the $x$-coefficients with equation (2):
$2(8x - 6y) = 2(-20)$
$16x - 12y = -40$

Now the system becomes:

1. $16x - 12y = -40$
2. $-16x + 7y = 30$

Add the two equations together:
$(16x - 12y) + (-16x + 7y) = -40 + 30$
$-5y = -10$

Solve for $y$:
$y = \frac{-10}{-5} = 2$

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Step 3: Solve for $x$

Substitute $y = 2$ into one of the original equations, such as $8x - 6y = -20$:
$8x - 6(2) = -20$
$8x - 12 = -20$
$8x = -8$
$x = \frac{-8}{8} = -1$

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Final Solution

The solution to the system is:
$x = -1, \, y = 2$

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Verification

Substitute $x = -1$ and $y = 2$ into both original equations:

1. $8(-1) - 6(2) = -8 - 12 = -20$ ✅
2. $-16(-1) + 7(2) = 16 + 14 = 30$ ✅

Thus, the solution is correct.

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Would you like more details or have questions?

Related Questions

1. How do you solve systems of equations using substitution?
2. What are the steps for solving a system of three equations?
3. Can you show graphing these equations and their intersection point?
4. How can elimination be used when the coefficients are not easily aligned?
5. Why does verifying the solution ensure accuracy?

Tip

When solving systems of equations, always verify the solution in both original equations to avoid errors.