Plz help The positions of two straight roads are
represented by the equations
5x + 3y = 25
- 3x + 5y = 19.
Solve the equation to find the position (x, y)
where the two roads intersect.

Step-by-step explanation:

To solve this system of equations, we can first start by solving for one of the two variables in one of the equations. Let's use the first equation to solve for our value:

Subtract   from both sides of the equation:

Divide both sides of the equation by the coefficient of , which is :

Now that we have our value, we can substitute it into the second equation to solve for our value:

Substitute:

Distribute the into the parentheses:

Combine the fractions by achieving a common denominator between and . (Multiply by ):

×

=

The equation now looks like:

Multiply both sides of the equation by to get rid of the fraction:

Add to both sides of the equation:

Divide both sides of the equation by the coefficient of , which is :

Now with our value, we can substitute into the equation representative of the value:

Substitute:

Multiply:

Divide:

Subtract:

Therefore, the two roads intersect at the position .

-

You can check your work by substituting the solved variable values into the initial system of equations:

Since the sides of the equations are equal to each other, our solution is correct!

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