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Solve the system of equations:

[tex]\[
\begin{cases}
x - 2y = 1 \\
3x + y = 3
\end{cases}
\][/tex]

Sagot :

GinnyAnsweridn
Sure, let's solve the given system of linear equations step-by-step.

We are given:
1) [tex]\( x - 2y = 1 \)[/tex]
2) [tex]\( 3x + y = 3 \)[/tex]

### Step 1: Solve the first equation for [tex]\( x \)[/tex]

From the first equation:
[tex]\[ x - 2y = 1 \][/tex]

We isolate [tex]\( x \)[/tex]:
[tex]\[ x = 1 + 2y \][/tex]

### Step 2: Substitute [tex]\( x = 1 + 2y \)[/tex] into the second equation

Now substitute [tex]\( x = 1 + 2y \)[/tex] into the second equation:
[tex]\[ 3(1 + 2y) + y = 3 \][/tex]

### Step 3: Simplify the substituted equation

Expand the equation:
[tex]\[ 3 + 6y + y = 3 \][/tex]
[tex]\[ 3 + 7y = 3 \][/tex]

Next, isolate [tex]\( y \)[/tex]:
[tex]\[ 7y = 3 - 3 \][/tex]
[tex]\[ 7y = 0 \][/tex]
[tex]\[ y = 0 \][/tex]

### Step 4: Substitute [tex]\( y = 0 \)[/tex] back into the equation for [tex]\( x \)[/tex]

Now that we have [tex]\( y = 0 \)[/tex], substitute it back into the expression we found for [tex]\( x \)[/tex]:
[tex]\[ x = 1 + 2y \][/tex]
[tex]\[ x = 1 + 2(0) \][/tex]
[tex]\[ x = 1 \][/tex]

### Conclusion

The solution to the system of equations is:
[tex]\[ x = 1 \][/tex]
[tex]\[ y = 0 \][/tex]

So the solution can be written as the ordered pair [tex]\((1, 0)\)[/tex].
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