To find the coordinates of the intersection point that solves the system of equations 2x + y = 15 and y = -x + 5, we can substitute the second equation into the first equation:
2x + (-x + 5) = 15
Combining like terms, we get:
x + 5 = 15
Subtracting 5 from both sides, we have:
x = 10
Now we can substitute the value of x back into either of the original equations. Let's use the second equation:
y = -x + 5
y = -(10) + 5
y = -10 + 5
y = -5
Therefore, the coordinates of the intersection point are (10, -5).
The answer is (10, -5).
Find the coordinates of the intersection point that solves the system of these two linear equations in two variables: 2x + y = 15 and y = -x + 5. Is the answer (-5 10-) (10 5) (10, -5) or (5 -10)
5 answers
Is (-2, 6) A solution to the system of these linear equations: x + 2y = 10 and 3x + y = 0 why? No because the grass don't intersect at (-2, 6) Yes because the graphs intersect at (-2, 6) Yes because the grass don't intersect at (-2, 6) No, because the graphs 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 need to substitute those values into the equations and check if they satisfy both equations.
First, let's substitute (-2, 6) into the first equation:
x + 2y = 10
-2 + 2(6) = 10
-2 + 12 = 10
10 = 10
The equation is true.
Now, let's substitute (-2, 6) into the second equation:
3x + y = 0
3(-2) + 6 = 0
-6 + 6 = 0
0 = 0
The equation is also true.
Therefore, (-2, 6) is indeed a solution to the system of equations.
The answer is Yes, because the graphs intersect at (-2, 6).
First, let's substitute (-2, 6) into the first equation:
x + 2y = 10
-2 + 2(6) = 10
-2 + 12 = 10
10 = 10
The equation is true.
Now, let's substitute (-2, 6) into the second equation:
3x + y = 0
3(-2) + 6 = 0
-6 + 6 = 0
0 = 0
The equation is also true.
Therefore, (-2, 6) is indeed a solution to the system of equations.
The answer is Yes, because the graphs intersect at (-2, 6).
What is the last step to solving a system of equations? Graph the lines, check the answer, estimate the intersection point or make a table of solutions of linear equations
The last step to solving a system of equations depends on the method used to solve them.
If you solve the system graphically, the last step would be to graph the lines representing the equations and visually determine the point of intersection.
If you solve the system algebraically, the last step may be to check the answer by substituting the values obtained into both equations to ensure they satisfy both.
If you use other methods, such as estimation or making a table of solutions, the last step would involve utilizing those methods to find the solution or verify the estimated intersection point or table values.
In summary, the last step to solving a system of equations can vary depending on the method used, but it often involves verifying the solution or estimating the intersection point.
If you solve the system graphically, the last step would be to graph the lines representing the equations and visually determine the point of intersection.
If you solve the system algebraically, the last step may be to check the answer by substituting the values obtained into both equations to ensure they satisfy both.
If you use other methods, such as estimation or making a table of solutions, the last step would involve utilizing those methods to find the solution or verify the estimated intersection point or table values.
In summary, the last step to solving a system of equations can vary depending on the method used, but it often involves verifying the solution or estimating the intersection point.