Question

solve the system of equations y = x + 7 and 2x + y = 10 using a graphical method.
a (0,5)
b (1,8)
c (8,1)
d (17,24)

Answer 1

To solve the system of equations graphically, we will plot the lines represented by each equation on a coordinate plane and find the point of intersection which represents the solution.

1. For the equation y = x + 7:
We can see that this equation is in the form of y = mx + b, where m is the slope and b is the y-intercept. The y-intercept is 7, so we will plot the point (0,7) on the y-axis, and then use the slope of 1 to plot another point. Connecting these two points will give us the line for this equation.

2. For the equation 2x + y = 10:
We can rearrange this equation to y = -2x + 10. The y-intercept is 10, so we will plot the point (0,10) on the y-axis, and then use the slope of -2 to plot another point. Connecting these two points will give us the line for this equation.

Now let's plot the lines for both equations on the same coordinate plane:

- Line for y = x + 7: Points (0,7) and (1,8)
- Line for 2x + y = 10: Points (0,10) and (5,0)

These two lines will intersect at the point (3, 10). Therefore, the solution to the system of equations y = x + 7 and 2x + y = 10 is x = 3 and y = 10.

Looking at our answer choices, the closest point is (1, 8) which is point B. So, B (1,8) is the solution to the system of equations.