Use the image to answer the question.
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 ().
the anwser is (3,8)
The intersection point is (3, 8).
To find the intersection point of the two lines, we can set their equations equal to each other and solve for the variables.
First, let's rewrite the equations of the two lines:
Solid line: y = x + 5
Dotted line: 4x + 3y = 15
Now, we will substitute the value of y from the solid line equation into the dotted line equation:
4x + 3(x + 5) = 15
Next, we simplify the equation:
4x + 3x + 15 = 15
7x + 15 = 15
Subtracting 15 from both sides, we get:
7x = 0
Dividing both sides by 7:
x = 0
Now that we have found the value of x, we can substitute it back into either of the original equations to find the value of y. Let's use the solid line equation:
y = x + 5
y = 0 + 5
y = 5
Therefore, the intersection point of the two lines is (0, 5).