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
To find the intersection point that solves the system of equations, we can substitute the value of y from the second equation into the first equation.
Given equations:
1) 2x + y = 15
2) y = -x + 5
Substituting the value of y from equation 2 into equation 1, we get:
2x + (-x + 5) = 15
2x - x + 5 = 15
x + 5 = 15
x = 15 - 5
x = 10
To find the value of y, we can substitute the value of x into equation 2:
y = -x + 5
y = -(10) + 5
y = -10 + 5
y = -5
Therefore, the intersection point of the two equations is (10, -5).
Is (−2, 6) a solution to the system of these linear equations: x+2y=10 and 3x+y=0 ? Why?
To determine if (-2, 6) is a solution to the system of linear equations, we substitute the values of x and y into each equation and check if both equations are satisfied.
Given equations:
1) x + 2y = 10
2) 3x + y = 0
Substituting (-2, 6) into equation 1:
-2 + 2(6) = 10
-2 + 12 = 10
10 = 10
Since both sides of the equation are equal, the first equation is satisfied when x = -2 and y = 6.
Substituting (-2, 6) into equation 2:
3(-2) + 6 = 0
-6 + 6 = 0
0 = 0
Again, both sides of the equation are equal, so the second equation is satisfied when x = -2 and y = 6.
Therefore, (-2, 6) is indeed a solution to the system of linear equations.
Estimate the solution to the system of these linear equations based on the graph. y=5x+10 y=−2x+3
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 first equation is y = 5x + 10, which has a slope of 5 and a y-intercept of 10. The second equation is y = -2x + 3, which has a slope of -2 and a y-intercept of 3.
By observing the graph of the two lines, we can see that they intersect at a point approximately (-1, 5).
Therefore, the estimated solution to the system of linear equations is (-1, 5).
What is the last step to solving a system of equations?
The last step to solving a system of equations is to check the solution by substituting the values for the variables back into the original equations. By doing this, we can ensure that the values we found for the variables satisfy both equations and are indeed a solution to the system. If the values satisfy both equations, then the solution is correct.
Estimate the solution to the system of these linear equations based on the graph. y=−5x+7 y=−2x+10
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 first equation is y = -5x + 7, which has a slope of -5 and a y-intercept of 7. The second equation is y = -2x + 10, which has a slope of -2 and a y-intercept of 10.
By observing the graph of the two lines, we can see that they intersect at a point approximately (1, 2).
Therefore, the estimated solution to the system of linear equations is (1, 2).