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Solve using substitution.

[tex]\[
\begin{array}{l}
y = -6 \\
-10x + 2y = 8
\end{array}
\][/tex]

Sagot :

GinnyAnsweridn
Sure, let's solve the given system of equations using the method of substitution step by step. The system of equations is:

[tex]\[ \begin{array}{l} y = -6 \\ -10x + 2y = 8 \end{array} \][/tex]

### Step-by-Step Solution:

1. Substitute [tex]\( y \)[/tex] from the first equation into the second equation:

We know from the first equation that [tex]\( y = -6 \)[/tex]. We substitute [tex]\( y = -6 \)[/tex] into the second equation:

[tex]\[-10x + 2(-6) = 8\][/tex]

2. Simplify the equation:

Now, simplify the left side of the equation:

[tex]\[-10x + 2 \cdot (-6) = -10x - 12\][/tex]

So, the equation becomes:

[tex]\[-10x - 12 = 8\][/tex]

3. Solve for [tex]\( x \)[/tex]:

To isolate [tex]\( x \)[/tex], first add 12 to both sides of the equation:

[tex]\[-10x - 12 + 12 = 8 + 12\][/tex]

This simplifies to:

[tex]\[-10x = 20\][/tex]

Next, divide both sides by -10:

[tex]\[x = \frac{20}{-10}\][/tex]

So, [tex]\( x = -2 \)[/tex].

4. State the values of [tex]\( x \)[/tex] and [tex]\( y \)[/tex]:

We have found [tex]\( x = -2 \)[/tex] and from the first equation we were given [tex]\( y = -6 \)[/tex].

### Conclusion:

The solution to the system of equations is:

[tex]\[ x = -2, \quad y = -6 \][/tex]

Thus, the ordered pair that satisfies both equations is [tex]\((-2, -6)\)[/tex].
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