Answered

IDNLearn.com provides a seamless experience for finding and sharing answers. Our experts provide timely, comprehensive responses to ensure you have the information you need.

What is the solution of the system?

[tex]
\left\{
\begin{array}{c}
4x - y = -38 \\
x + y = 3
\end{array}
\right.
[/tex]

Enter your answer in the boxes.

Sagot :

GinnyAnsweridn
To solve the system of equations:

[tex]\[ \begin{cases} 4x - y = -38 \\ x + y = 3 \end{cases} \][/tex]

we will use the method of substitution or elimination. Let's go through the steps in detail:

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

Let's solve the second equation for [tex]\( y \)[/tex]:

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

Subtract [tex]\( x \)[/tex] from both sides:

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

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

Now substitute [tex]\( y = 3 - x \)[/tex] into the first equation [tex]\( 4x - y = -38 \)[/tex]:

[tex]\[ 4x - (3 - x) = -38 \][/tex]

Simplify inside the parentheses:

[tex]\[ 4x - 3 + x = -38 \][/tex]

Combine like terms:

[tex]\[ 5x - 3 = -38 \][/tex]

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

Add 3 to both sides to isolate the term with [tex]\( x \)[/tex]:

[tex]\[ 5x = -35 \][/tex]

Divide both sides by 5:

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

Step 4: Substitute [tex]\( x = -7 \)[/tex] back into the expression for [tex]\( y \)[/tex] to find [tex]\( y \)[/tex].

Substitute [tex]\( x = -7 \)[/tex] into the equation [tex]\( y = 3 - x \)[/tex]:

[tex]\[ y = 3 - (-7) \][/tex]

Simplify:

[tex]\[ y = 3 + 7 \][/tex]

[tex]\[ y = 10 \][/tex]

Conclusion:

The solution to the system of equations is:
[tex]\[ x = -7 \][/tex]
[tex]\[ y = 10 \][/tex]

Therefore, the values in the boxes should be:
[tex]\[ x = -7 \quad \text{and} \quad y = 10 \][/tex]
We appreciate your presence here. Keep sharing knowledge and helping others find the answers they need. This community is the perfect place to learn together. IDNLearn.com provides the answers you need. Thank you for visiting, and see you next time for more valuable insights.