Use the image to answer the question.

4x + 3y = 15
y = x + 5
Review the graphs of a system of two linear equations in two variables: 4x + 3y = 15 and y = x + 5. Find the solution to both equations.
The intersection point is (__).

1 answer

To find the solution to the system of equations given by \(4x + 3y = 15\) and \(y = x + 5\), we will substitute \(y\) from the second equation into the first one.

  1. Substituting \(y\): \[ y = x + 5 \] Substitute \(y\) in the first equation: \[ 4x + 3(x + 5) = 15 \]

  2. Simplifying the equation: \[ 4x + 3x + 15 = 15 \] \[ 7x + 15 = 15 \] Now, subtract 15 from both sides: \[ 7x = 0 \] Dividing by 7 gives: \[ x = 0 \]

  3. Finding \(y\): Substitute \(x = 0\) back into the equation for \(y\): \[ y = 0 + 5 = 5 \]

Therefore, the solution to both equations, or the intersection point, is \((0, 5)\).

So, the final answer is: The intersection point is (0, 5).