Answer :

GinnyAnswer
Let's solve the system of equations using the method of substitution. Here are the equations:

[tex]\[ \begin{cases} -2 x + y = -5 \\ -4 y = 22 - 8 x \end{cases} \][/tex]

### Step 1: Solve one of the equations for one variable

We start by solving the first equation for [tex]\( y \)[/tex]:

[tex]\[ -2 x + y = -5 \implies y = 2x - 5 \][/tex]

### Step 2: Substitute the expression for [tex]\( y \)[/tex] into the second equation

Next, we substitute [tex]\( y = 2x - 5 \)[/tex] into the second equation:

[tex]\[ -4 (2x - 5) = 22 - 8x \][/tex]

### Step 3: Simplify the substituted equation and solve for [tex]\( x \)[/tex]

First, expand and simplify the equation:

[tex]\[ -4 (2x - 5) = 22 - 8x \\ -8x + 20 = 22 - 8x \][/tex]

Notice that the terms [tex]\(-8x\)[/tex] on both sides cancel each other out:

[tex]\[ 20 = 22 \][/tex]

This is a contradiction because 20 does not equal 22. Therefore, the system of equations has no solution.

### Conclusion:

Since we have derived a contradiction, it indicates that the system of equations is inconsistent and there are no solutions.

[tex]\[ \text{No solutions} \][/tex]

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