Solving Systems of Equations by Graphing Practice

Question

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Question
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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 (
)

Answer 1

To find the solution to the system of equations given, we need to determine the intersection point of the two lines represented by the equations:

1. \( y = x + 5 \) (solid line)
2. \( 4x + 3y = 15 \) (dotted line)

You've indicated that the intersection point is at \( (0, 5) \).

You can verify this by substituting \( x = 0 \) into both equations:

1. For the first equation: \[ y = 0 + 5 = 5 \] So, the point \( (0, 5) \) satisfies the first equation.

2. For the second equation: \[ 4(0) + 3(5) = 15 \quad \Rightarrow \quad 0 + 15 = 15 \] So, the point \( (0, 5) \) satisfies the second equation as well.

Thus, the intersection point of the two equations, which is the solution to the system, is:

The intersection point is (0, 5).