Estimate the solution to the system of these linear equations based on the graph. y=5x+10 y=−2x+3 (1 point) Responses (−1,−5) left parenthesis negative 1 comma negative 5 right parenthesis (5,−1) left parenthesis 5 comma negative 1 right parenthesis (−1, 5) left parenthesis negative 1 comma 5 right parenthesis (1, 5)
Based on the graph and the equations, we can estimate that the solution to the system is approximately (1, 5).
Are you sure?
I apologize for the confusion. After reevaluating the equations, the correct estimate for the solution to the system is (-1, -5).
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Estimate the solution to the system of these linear equations based on the graph. y=5x+10 y=−2x+3 (1 point)
(−1,−5)
(5,−1)
(−1, 5)
(1, 5)
Based on the graph, the estimated solution to the system of linear equations is (-1, -5).
Is (−2, 6) a solution to the system of these linear equations: x+2y=10 and 3x+y=0 ? Why?(1 point) Responses Yes, because the graphs don’t intersect at (−2, 6). Yes, because the graphs don’t intersect at left parenthesis negative 2 comma 6 right parenthesis . Yes, because the graphs intersect at (−2, 6). Yes, because the graphs intersect at left parenthesis negative 2 comma 6 right parenthesis . No, because the graphs intersect at (−2, 6). No, because the graphs intersect at left parenthesis negative 2 comma 6 right parenthesis . No, because the graphs don’t intersect at (−2, 6
To determine if (−2, 6) is a solution to the system of equations x+2y=10 and 3x+y=0, we can substitute the values of x and y into both equations and see if the equations hold true.
Substituting x = -2 and y = 6 into the first equation:
(-2) + 2(6) = 10
-2 + 12 = 10
10 = 10
Substituting x = -2 and y = 6 into the second equation:
3(-2) + 6 = 0
-6 + 6 = 0
0 = 0
Since both equations are true when x = -2 and y = 6, (−2, 6) is indeed a solution to the system of linear equations. Therefore, the correct response is Yes, because the graphs intersect at (−2, 6).
What is the last step to solving a system of equations?(1 point) Responses Check the answer. Check the answer. Make a table of solutions of the linear equations. Make a table of solutions of the linear equations. Graph the lines. Graph the lines. Estimate the intersection point.
The last step to solving a system of equations is to check the answer. This involves substituting the values of the variables back into the original equations to ensure they satisfy both equations. Therefore, the correct response is Check the answer.
To estimate the solution to the system of linear equations based on the graph, we need to find the point where the two lines intersect. The point of intersection represents the solution to the system.
Looking at the given equations:
1) y = 5x + 10
2) y = -2x + 3
We can determine the solution by finding the x-coordinate and y-coordinate of the point where the lines intersect.
By setting the two equations equal to each other, we can solve for x:
5x + 10 = -2x + 3
Rearranging the equation, we get:
5x + 2x = 3 - 10
7x = -7
x = -7/7
x = -1
Now that we have the value of x, we can substitute it back into either of the given equations to find the y-coordinate. Let's use equation 1:
y = 5(-1) + 10
y = -5 + 10
y = 5
Therefore, the estimated solution to the system of linear equations based on the graph is (-1, 5).