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Use any method to solve the system.

[tex]
\begin{array}{c}
\left\{\begin{array}{l}
3x - 5y = 16 \\
2x + y = 15
\end{array}\right. \\
(x, y) = (\square)
\end{array}
[/tex]

Sagot :

GinnyAnswer
Sure! Let's solve the system of linear equations step by step.

Given the system of equations:

[tex]\[ \begin{cases} 3x - 5y = 16 \\ 2x + y = 15 \end{cases} \][/tex]

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

We can solve the second equation for [tex]\( y \)[/tex]:

[tex]\[ 2x + y = 15 \implies y = 15 - 2x \][/tex]

### Step 2: Substitute [tex]\( y \)[/tex] into the first equation

Now we'll substitute [tex]\( y = 15 - 2x \)[/tex] into the first equation:

[tex]\[ 3x - 5(15 - 2x) = 16 \][/tex]

### Step 3: Simplify and solve for [tex]\( x \)[/tex]

Expand and simplify the equation:

[tex]\[ 3x - 75 + 10x = 16 \implies 13x - 75 = 16 \implies 13x = 91 \implies x = \frac{91}{13} \][/tex]

So,

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

### Step 4: Substitute [tex]\( x \)[/tex] back to find [tex]\( y \)[/tex]

Now we use [tex]\( x = 7 \)[/tex] in the equation [tex]\( y = 15 - 2x \)[/tex]:

[tex]\[ y = 15 - 2(7) \implies y = 15 - 14 \implies y = 1 \][/tex]

### Conclusion

The solution to the system of equations is:

[tex]\[ (x, y) = (7, 1) \][/tex]

So the answer is:

[tex]\[ (x, y) = (7, 1) \][/tex]
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