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Find the solution of this system of equations. Separate the [tex]$x$[/tex]- and [tex]$y$[/tex]-values with a comma.

[tex]\[
\begin{array}{c}
x - 2y = -23 \\
x - y = 7
\end{array}
\][/tex]

Enter the correct answer.


Sagot :

To find the solution to the system of equations given by:

[tex]\[ \begin{aligned} &1.\; x - 2y = -23 \\ &2.\; x - y = 7 \\ \end{aligned} \][/tex]

we can use the method of substitution or elimination. Here is a step-by-step method to solve it using elimination:

1. Step 1: Align the equations for elimination

[tex]\[ \begin{aligned} &1.\; x - 2y = -23 \quad \text{(Equation 1)} \\ &2.\; x - y = 7 \quad \text{(Equation 2)} \end{aligned} \][/tex]

2. Step 2: Eliminate one variable

To eliminate the variable [tex]\( x \)[/tex], we subtract Equation 2 from Equation 1:

[tex]\[ (x - 2y) - (x - y) = -23 - 7 \][/tex]

Simplifying this, we get:

[tex]\[ x - 2y - x + y = -23 - 7 \][/tex]

[tex]\[ -y = -30 \][/tex]

[tex]\[ y = 30 \][/tex]

3. Step 3: Substitute the value of [tex]\( y \)[/tex] back into one of the original equations

We can use Equation 2 for substitution:

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

Substituting [tex]\( y = 30 \)[/tex]:

[tex]\[ x - 30 = 7 \][/tex]

Solving for [tex]\( x \)[/tex]:

[tex]\[ x = 37 \][/tex]

4. Step 4: Verify the solution

Use the values [tex]\( x = 37 \)[/tex] and [tex]\( y = 30 \)[/tex] to check both original equations:

[tex]\[ \text{Equation 1: } 37 - 2(30) = 37 - 60 = -23 \quad \text{(Correct)} \][/tex]

[tex]\[ \text{Equation 2: } 37 - 30 = 7 \quad \text{(Correct)} \][/tex]

Thus, the solution to the system of equations is:

[tex]\[ \boxed{37, \ 30} \][/tex]