Solve the system of linear equations by substitution: x = 17 - 4y, y = x - 2. The solution is: ( , )

Understand the Problem

The question is asking to solve a system of linear equations using the substitution method. It requires finding the values of x and y that satisfy both equations provided.

Answer

The solution is $(5, 3)$.

Steps to Solve

Substitute the expression for y in terms of x

We know from the second equation that $y = x - 2$. Substitute this expression for $y$ into the first equation.

$$ x = 17 - 4(x - 2) $$

Simplify the equation

Distribute $-4$ in the equation:

$$ x = 17 - 4x + 8 $$

Combine like terms:

$$ x + 4x = 25 $$

This simplifies to:

$$ 5x = 25 $$

Solve for x

Now divide both sides by 5 to find the value of $x$:

$$ x = \frac{25}{5} $$

Thus,

$$ x = 5 $$

Substitute to find y

Now substitute the value of $x$ back into the equation for $y$:

$$ y = 5 - 2 $$

This simplifies to:

$$ y = 3 $$

Write the final solution

The solution to the system of equations is:

$$(x, y) = (5, 3)$$

The solution is: $(5, 3)$

More Information

The solution $(5, 3)$ represents the point where the two lines described by the equations intersect on a coordinate plane. This means that when $x = 5$, $y$ will be $3$ for both equations.

Tips

Failing to substitute correctly into the first equation.
Incorrectly distributing or combining like terms. Always double-check arithmetic when manipulating equations.

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