How do you find the solution to a system of equations graphically? (1 point)
Find the point where the two lines intersect
Find the slope of the two lines
Find the y-intercept of the two lines
Find the slope and y-intercept of the two lines
To solve the system of equations:
1) Substitute the value of y from the second equation into the first equation:
8x - 3(10 + 4x) = -22
2) Simplify the equation by distributing the -3:
8x - 30 - 12x = -22
3) Combine like terms:
-4x - 30 = -22
4) Add 30 to both sides:
-4x = 8
5) Divide by -4 to solve for x:
x = -2
6) Substitute the value of x into either equation to solve for y:
y = 10 + 4(-2)
y = 10 - 8
y = 2
Therefore, the solution to the system of equations is x = -2 and y = 2.
Find the point where the two lines intersect
What will the graph look like for a system of equations that has no solution? (1 point)
You will see perpendicular lines
You will see the lines intersect at two different points
You will see lines on top of each other so that they form the same exact lineYou will see the lines intersect at only one point
You will see parallel lines
You will see parallel lines
Solving the system y--+3 and z+y-8 by graphing shows that there is no solution to the systemIs this statement true or false? Explain
(1 point)
The statement is falsebecause the lines have an intersection point
The statement is false, because the lines are parallel
The statement is true because the Ines are parallel
The statement is true because the lines have an intersection point
The statement is false, because there is not enough information provided. We would need to plot the equations or at least examine them more closely to determine the relationship between them.
Solve the given system of linear equations by inspection
COURSE TOOLS
(1 point)
infinitely many solutions
0 (-5,
6(65)
no solution
Without the specific system of linear equations provided, it is not possible to determine the solution by inspection. Please provide the equations to solve.
Solve the system of equations
8x - 3y = - 22
y=10+4x
Solve the system of equations
5x+2y=14
x-6y=22
Solve the system of equations
—9x+y=12
2x+4y=-28
Solve the system of equations
6x+2y=-18
3x+y=24
To solve the system of equations:
1) Multiply the second equation by 2 to make the coefficients of y the same:
2(x - 6y) = 2(22)
2x - 12y = 44
2) Add the equations together to eliminate x:
(5x + 2y) + (2x - 12y) = 14 + 44
7x - 10y = 58
3) Solve the resulting equation for x or y:
7x - 10y = 58
4) Solve for x in terms of y:
7x = 10y + 58
x = (10y + 58)/7
5) Substitute this value of x into either equation to solve for y:
5((10y + 58)/7) + 2y = 14
(50y + 290)/7 + 2y = 14
(50y + 290 + 14(7))/(7) = 14
(50y + 290 + 98)/7 = 14
(50y + 388)/7 = 14
50y + 388 = 98(14)
50y + 388 = 1372
50y = 1372 - 388
50y = 984
y = 984/50
y = 19.68
6) Substitute the value of y back into either equation to solve for x:
5x + 2(19.68) = 14
5x + 39.36 = 14
5x = 14 - 39.36
5x = -25.36
x = -25.36/5
x = -5.07
Therefore, the solution to the system of equations is x = -5.07 and y = 19.68.
To solve the system of equations:
1) Multiply the first equation by 4 to make the coefficients of y the same:
4(-9x + y) = 4(12)
-36x + 4y = 48
2) Add the equations together to eliminate y:
(2x + 4y) + (-36x + 4y) = -28 + 48
-34x = 20
3) Solve for x:
x = 20/(-34)
x = -10/17
4) Substitute the value of x into either equation to solve for y:
-9(-10/17) + y = 12
90/17 + y = 12
y = 12 - 90/17
y = (204 - 90)/17
y = 114/17
Therefore, the solution to the system of equations is x = -10/17 and y = 114/17.
We could solve the system of equations using the method of substitution or the method of elimination. Here, I will solve it using the method of substitution:
1) Solve one equation for a variable in terms of the other variable. Let's solve the second equation for y:
y = 24 - 3x
2) Substitute the expression for y into the first equation:
6x + 2(24 - 3x) = -18
3) Distribute and simplify the equation:
6x + 48 - 6x = -18
48 = -18
4) Since 48 does not equal -18, there is no solution to this system of equations.
Therefore, the system of equations is inconsistent and has no solution.