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Substitution Homework

Solve the following systems of equations. Write your answer as a coordinate pair [tex]\((x, y)\)[/tex].

1.
[tex]\[
\begin{array}{l}
y = 6x \\
-x + 2y = -11
\end{array}
\][/tex]

Solution: \(\_\_\_\_\_\_\_)

Sagot :

GinnyAnsweridn
Let's solve the given system of equations step-by-step. The system is:

[tex]\[ \begin{array}{l} y = 6x \quad \text{(Equation 1)} \\ -x + 2y = -11 \quad \text{(Equation 2)} \end{array} \][/tex]

### Step 1: Substitute [tex]\( y \)[/tex] from Equation 1 into Equation 2

Since Equation 1 tells us that [tex]\( y = 6x \)[/tex], we can substitute [tex]\( 6x \)[/tex] for [tex]\( y \)[/tex] in Equation 2. This gives us:

[tex]\[ -x + 2(6x) = -11 \][/tex]

### Step 2: Simplify the resulting equation

Now, distribute the 2 in [tex]\( 2(6x) \)[/tex]:

[tex]\[ -x + 12x = -11 \][/tex]

Combine the like terms:

[tex]\[ 11x = -11 \][/tex]

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

Divide both sides of the equation by 11:

[tex]\[ x = \frac{-11}{11} = -1 \][/tex]

So, the value of [tex]\( x \)[/tex] is [tex]\( -1 \)[/tex].

### Step 4: Substitute [tex]\( x \)[/tex] back into Equation 1 to find [tex]\( y \)[/tex]

Now that we have [tex]\( x = -1 \)[/tex], substitute it back into Equation 1 to find [tex]\( y \)[/tex]:

[tex]\[ y = 6(-1) = -6 \][/tex]

So, the value of [tex]\( y \)[/tex] is [tex]\( -6 \)[/tex].

### Final Solution

Thus, the solution to the system of equations is:

[tex]\[ (x, y) = (-1, -6) \][/tex]
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