Solve -7x - 2y = -15, y = -10.

Understand the Problem

The question is asking to solve the given system of equations, which includes one equation in two variables involving x and y. It specifies y value already, which can be substituted into the first equation to find x.

Answer

$(5, -10)$

Steps to Solve

Substitute the value of y

We know that $y = -10$. We can substitute this value into the equation $-7x - 2y = -15$.

Replace y in the equation

By substituting $y = -10$, we modify the equation:

$$ -7x - 2(-10) = -15 $$

Simplify the equation

Now, simplify the equation:

$$ -7x + 20 = -15 $$

Isolate x

Next, subtract 20 from both sides to isolate the term with $x$:

$$ -7x = -15 - 20 $$

This simplifies to:

$$ -7x = -35 $$

Solve for x

Now, divide both sides by -7:

$$ x = \frac{-35}{-7} $$

Which simplifies to:

$$ x = 5 $$

Write the solution as an ordered pair

The solution to the system of equations is $(5, -10)$.

The solution is $(5, -10)$.

More Information

This solution represents the point where the two equations intersect on the coordinate plane. Substituting the known value of $y$ into the equation simplifies the problem, allowing us to solve for $x$ easily.

Tips

Incorrect substitution: Ensure that the value of $y$ is substituted correctly and sign adjustments are made accurately.
Oversight in signs: Be careful with negative signs when adding or subtracting them in equations.

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