Question

Solve the following system of
equations by graphing.
𝑦 = −𝑥 + 5
𝑦 = 2𝑥 − 4
E. (3, 2)
F. (1, 4)
G. (6, -1)

Answer 1

what letter do i pick
E.(3,2)
F.(1,4)
G.(6,-1)

Answer 2

To solve this system of equations by graphing, we will first graph each of the equations on the same set of axes and then identify the points where the graphs intersect.

The first equation is y = -x + 5. To graph this equation, plot the y-intercept at (0, 5) and then use the slope of -1 (rise of -1 and run of 1) to plot another point. Connect the points with a line.

The second equation is y = 2x - 4. To graph this equation, plot the y-intercept at (0, -4) and then use the slope of 2 (rise of 2 and run of 1) to plot another point. Connect the points with a line.

Now, look for the point where the two lines intersect. This point represents the solution to the system of equations.

The point of intersection is (3, 2). This means that the solution to the system of equations is x = 3 and y = 2.

Now, let's check the other given points to see which ones lie on both lines.

F. (1, 4):
For y = -x + 5: y = -1 + 5 = 4
For y = 2x - 4: y = 2(1) - 4 = 2 - 4 = -2
Since the y-values do not match, (1, 4) is not a solution to the system.

G. (6, -1):
For y = -x + 5: y = -6 + 5 = -1
For y = 2x - 4: y = 2(6) - 4 = 12 - 4 = 8
Since the y-values do not match, (6, -1) is not a solution to the system.

Therefore, the solution to the system of equations is E. (3, 2).

Answer 3

You would pick the letter E, as it corresponds to the point (3, 2) which is the solution to the system of equations.