Question

Use linear systems to determine where the \(x\) -coordinate is equal to the \(y\) -coordinate on the graph of \(2 x+3 y=25\).

Short answer

The point on the graph of \(2x + 3y = 25\) where the x-coordinate equals the y-coordinate is (5,5).

Step-by-step solution

Specify the Coordinates

The coordinates that we need to find are where the x and y are equal. Let's represent these equal coordinates as \(a\). Therefore the coordinates become \((a, a)\).

Substitute into the Equation

Substitute \(a\) for \(x\) and \(y\) in the equation \(2x + 3y = 25\) to derive a new equation. This results in the equation \(2a + 3a = 25\).

Solve for 'a'

Combine like terms to get \(5a = 25\). Then divide by 5 to solve for \(a\), so \(a = 5\). Therefore, the coordinates (x,y) on the line where x=y are (5,5).