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Solve the system:
[tex]\[
\begin{array}{c}
2x - y = -19 \\
-3x + 5y = 39
\end{array}
\][/tex]


Sagot :

To solve the system of equations:
[tex]\[ \begin{array}{c} 2x - y = -19 \\ -3x + 5y = 39 \end{array} \][/tex]

we can follow these steps:

### 1. Write down the system of equations:
[tex]\[ \begin{array}{c} 2x - y = -19 \quad \text{(Equation 1)} \\ -3x + 5y = 39 \quad \text{(Equation 2)} \end{array} \][/tex]

### 2. Solve for [tex]\( y \)[/tex] in terms of [tex]\( x \)[/tex] from Equation 1:

Start with Equation 1:
[tex]\[ 2x - y = -19 \][/tex]

Isolate [tex]\( y \)[/tex]:
[tex]\[ y = 2x + 19 \][/tex]

### 3. Substitute [tex]\( y \)[/tex] into Equation 2:

Now take the expression for [tex]\( y \)[/tex] from Equation 1 and substitute it into Equation 2:
[tex]\[-3x + 5(2x + 19) = 39\][/tex]

### 4. Simplify and solve for [tex]\( x \)[/tex]:

Expand the terms in the equation:
[tex]\[-3x + 10x + 95 = 39\][/tex]

Combine like terms:
[tex]\[ 7x + 95 = 39 \][/tex]

Subtract 95 from both sides:
[tex]\[ 7x = 39 - 95 \][/tex]
[tex]\[ 7x = -56 \][/tex]

Divide by 7:
[tex]\[ x = -8 \][/tex]

### 5. Substitute [tex]\( x \)[/tex] back into the expression for [tex]\( y \)[/tex]:

Substitute [tex]\( x = -8 \)[/tex] into [tex]\( y = 2x + 19 \)[/tex]:
[tex]\[ y = 2(-8) + 19 \][/tex]
[tex]\[ y = -16 + 19 \][/tex]
[tex]\[ y = 3 \][/tex]

### 6. State the solution:

The solution to the system of equations is:
[tex]\[ x = -8 \][/tex]
[tex]\[ y = 3 \][/tex]

So, the values that satisfy both equations are [tex]\( x = -8 \)[/tex] and [tex]\( y = 3 \)[/tex].
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