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A coordinate plane with four quadrants shows the x-axis ranging from negative 10 to 10 in increments of 1 and the y-axis ranging from negative 5 to 15 in increments of 1. A solid line and a dotted line intersect each other. The equation of the solid line is y equals x plus 5. The equation of the dotted line is 4 x plus 3 y equals 15. The intersection point of both lines is shown at 0 on the x-axis and positive 5 on the y-axis.

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.

(1 point)
The intersection point is (
a
)

1 answer

To find the intersection point of the two equations \( y = x + 5 \) and \( 4x + 3y = 15 \), we can substitute the value of \( y \) from the first equation into the second equation.

  1. Start with the first equation: \[ y = x + 5 \]

  2. Substitute \( y \) into the second equation \( 4x + 3y = 15 \): \[ 4x + 3(x + 5) = 15 \]

  3. Distribute and simplify: \[ 4x + 3x + 15 = 15 \] \[ 7x + 15 = 15 \]

  4. Isolate \( x \): \[ 7x = 15 - 15 \] \[ 7x = 0 \] \[ x = 0 \]

  5. Now substitute \( x = 0 \) back into the first equation to find \( y \): \[ y = 0 + 5 = 5 \]

The intersection point is \( (0, 5) \).

Thus, the answer is: The intersection point is \( (0, 5) \).