Answered

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Solve the following system of equations:

[tex]\[
\begin{cases}
2x + 3y = 5 \\
2x - y = -7
\end{cases}
\][/tex]

Sagot :

GinnyAnswer
Certainly! Let's solve the given system of linear equations step-by-step:

[tex]\[ \begin{cases} 2x + 3y = 5 \\ 2x - y = -7 \end{cases} \][/tex]

### Step 1: Express [tex]\( y \)[/tex] from the second equation.

First, we solve the second equation for [tex]\( y \)[/tex]:

[tex]\[ 2x - y = -7 \][/tex]

Rearrange to solve for [tex]\( y \)[/tex]:

[tex]\[ -y = -7 - 2x \][/tex]

Multiply by [tex]\(-1\)[/tex] to isolate [tex]\( y \)[/tex]:

[tex]\[ y = 7 + 2x \][/tex]

### Step 2: Substitute [tex]\( y \)[/tex] into the first equation.

Now we substitute [tex]\( y = 7 + 2x \)[/tex] into the first equation:

[tex]\[ 2x + 3(7 + 2x) = 5 \][/tex]

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

Distribute the 3 in the equation:

[tex]\[ 2x + 21 + 6x = 5 \][/tex]

Combine like terms:

[tex]\[ 8x + 21 = 5 \][/tex]

Subtract 21 from both sides:

[tex]\[ 8x = 5 - 21 \][/tex]

[tex]\[ 8x = -16 \][/tex]

Divide by 8:

[tex]\[ x = -2 \][/tex]

### Step 4: Solve for [tex]\( y \)[/tex].

Substitute [tex]\( x = -2 \)[/tex] back into the equation for [tex]\( y \)[/tex]:

[tex]\[ y = 7 + 2(-2) \][/tex]

Simplify:

[tex]\[ y = 7 - 4 \][/tex]

[tex]\[ y = 3 \][/tex]

### Solution

The solution to the system of equations is:

[tex]\[ (x, y) = (-2, 3) \][/tex]
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