How do you find the solution to a system of equations graphically?(1 point) Responses Find the slope of the two lines. Find the slope of the two lines. Find the slope and y-intercept of the two lines. Find the slope and y-intercept of the two lines. Find the y-intercept of the two lines. Find the y-intercept of the two lines. Find the point where the two lines intersect. Find the point where the two lines intersect.
The correct answer is: Find the point where the two lines intersect.
What will the graph look like for a system of equations that has no solution?(1 point) Responses You will see the lines intersect at two different points. You will see the lines intersect at two different points. You will see perpendicular lines. You will see perpendicular lines. You will see lines on top of each other so that they form the same exact line. You will see lines on top of each other so that they form the same exact line. You will see parallel lines. You will see parallel lines. You will see the lines intersect at only one point.
The correct answer is: You will see parallel lines.
Georgia Connections Academy is selling tickets to its Spring Fling. Adult tickets cost $4 and student tickets cost $2.50. The school makes $2,820. Write an equation that represents this situation to find the cost of all adult and student tickets sold. Use the variable s for student tickets and a for adult tickets sold. (7 points) Put responses in the correct input to answer the question. Select a response, navigate to the desired input and insert the response. Responses can be selected and inserted using the space bar, enter key, left mouse button or touchpad. Responses can also be moved by dragging with a mouse. Write an equation that represents this situation to find the cost of all adult and student tickets sold. Use the variable s for student tickets and a for adult tickets sold.
The equation that represents this situation to find the cost of all adult and student tickets sold is:
4a + 2.50s = 2820
900 tickets are sold for the spring fling. Write an equation to represent this situation. a + Response area =
a + s = 900
Use the above system of equations to determine how many adult and student tickets were sold. Response area adult tickets and Response area student tickets were sold.
To determine how many adult and student tickets were sold, we can solve the system of equations:
4a + 2.50s = 2820
a + s = 900
There are multiple methods to solve this system of equations. One method is substitution.
We can solve the second equation for a in terms of s:
a = 900 - s
Substitute this value of a into the first equation:
4(900 - s) + 2.50s = 2820
Simplify:
3600 - 4s + 2.50s = 2820
-1.50s = -780
s = 520
Substitute this value of s into the second equation to find a:
a + 520 = 900
a = 900 - 520
a = 380
Therefore, 380 adult tickets and 520 student tickets were sold.
To find the solution to a system of equations graphically, you need to find the point where the two lines intersect. Here's how you can do it:
1. Graph both equations on the same coordinate plane. Make sure to label the axes and choose appropriate scales.
2. Identify the slope and y-intercept of each line. The slope-intercept form of a linear equation is y = mx + b, where m represents the slope and b represents the y-intercept.
3. Plot the y-intercept of each line on the graph. The y-intercept is the point where the line crosses the y-axis, so it will have an x-coordinate of 0 and a y-coordinate equal to the y-intercept value.
4. Use the slope to draw the rest of each line. The slope tells you how the line increases or decreases as you move along the x-axis. For example, if the slope is positive, the line goes up as you move to the right; if the slope is negative, the line goes down as you move to the right.
5. Determine the point where the two lines intersect. This is the solution to the system of equations. It represents the values of x and y that make both equations true at the same time.
6. Read the coordinates of the intersection point from the graph. The x-coordinate gives you the value of x in the solution, and the y-coordinate gives you the value of y.
By following these steps, you will be able to find the solution to a system of equations graphically.