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Solve the system of equations:

[tex]\[
\begin{array}{l}
y = 4x + 3 \\
y = -x - 2
\end{array}
\][/tex]

Sagot :

GinnyAnswer
To solve the system of linear equations given by:

[tex]\[ \begin{array}{l} y = 4x + 3 \\ y = -x - 2 \end{array} \][/tex]

we need to find the values of [tex]\(x\)[/tex] and [tex]\(y\)[/tex] that satisfy both equations simultaneously.

1. Step 1: Set the right-hand sides of the equations equal to each other because they both equal [tex]\(y\)[/tex].

[tex]\[ 4x + 3 = -x - 2 \][/tex]

2. Step 2: Solve for [tex]\(x\)[/tex].

First, add [tex]\(x\)[/tex] to both sides to get:

[tex]\[ 4x + x + 3 = -2 \][/tex]

which simplifies to:

[tex]\[ 5x + 3 = -2 \][/tex]

Next, subtract 3 from both sides:

[tex]\[ 5x = -2 - 3 \][/tex]

which simplifies to:

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

Finally, divide both sides by 5 to isolate [tex]\(x\)[/tex]:

[tex]\[ x = -1 \][/tex]

3. Step 3: Substitute the value of [tex]\(x\)[/tex] back into one of the original equations to solve for [tex]\(y\)[/tex]. We'll use the first equation [tex]\(y = 4x + 3\)[/tex]:

[tex]\[ y = 4(-1) + 3 \][/tex]

which simplifies to:

[tex]\[ y = -4 + 3 \][/tex]

[tex]\[ y = -1 \][/tex]

So, the solution to the system of equations is:

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