Solve the system of linear equations by substitution. 2x - 3y = -9 x - 5y = -29 The solution is: ( , )

Understand the Problem

The question is asking to solve a system of linear equations using the substitution method. It provides two equations: 2x - 3y = -9 and x - 5y = -29, and requires the user to find the values of x and y.

Answer

The solution is $(6, 7)$.

Steps to Solve

Isolate one variable

Start with the second equation:

$$ x - 5y = -29 $$

Rearranging gives:

$$ x = -29 + 5y $$

Substitute into the first equation

Now substitute $x$ from the previous step into the first equation:

$$ 2(-29 + 5y) - 3y = -9 $$

Simplify the equation

Distribute the $2$:

$$ -58 + 10y - 3y = -9 $$

This simplifies to:

$$ -58 + 7y = -9 $$

Solve for $y$

Add $58$ to both sides:

$$ 7y = 49 $$

Then divide by $7$:

$$ y = 7 $$

Substitute $y$ back to find $x$

Now substitute $y = 7$ back into the equation for $x$:

$$ x = -29 + 5(7) $$

Calculating gives:

$$ x = -29 + 35 = 6 $$

The solution is: $(6, 7)$.

More Information

The solution $(6, 7)$ means that when $x = 6$ and $y = 7$, both equations will be satisfied. Substitution is a useful method for solving systems of equations when one variable can easily be isolated.

Tips

Forgetting to distribute correctly when substituting.
Miscalculating when isolating or solving for a variable.
Not substituting back into the correct original equation.

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