Part A
From the following system of equations, create a new equation by substituting the value of y from the first equation into the second equation.
From the new equation, evaluate the value of x.
y=−x−4
3x+y=8
Choose the correct option
(1 point)
Responses
x=6
x=8
x=12
x=3
To substitute the value of y from the first equation into the second equation, we can replace y in the second equation with (-x-4).
So, the new equation becomes: 3x + (-x-4) = 8.
Simplifying the equation: 3x - x - 4 = 8.
Combining like terms: 2x - 4 = 8.
Adding 4 to both sides of the equation: 2x = 12.
Dividing both sides of the equation by 2: x = 6.
So, the correct answer is x=6.
Part B
Note: Determine whether the solution to the new equation is a solution to the old system of equations by graphing. Use Desmos!
(1 point)
The solution to the original system of equations
is also
is not
a solution to the new equation.
Question 3
Solve the system of equations by SUBSTITUTION.
6y+5x=8
x+3y=−7
(1 point)
What would your equation look like after the first substitution
6y+5(3y-7)=8
6y+5(-3y-7)=8
6(-3y-7)+5x=8
6(3y-7)+5x=-7
To solve the system of equations by substitution, we can solve one equation for one variable and substitute it into the other equation.
Let's solve the second equation for x:
x + 3y = -7
x = -7 - 3y
Now we can substitute this expression for x in the first equation:
6y + 5x = 8
6y + 5(-7 - 3y) = 8
Simplifying the equation further:
6y - 35 - 15y = 8
-9y - 35 = 8
-9y = 8 + 35
-9y = 43
y = 43 / -9
y = -4.7778 (rounded to four decimal places)
Now we can substitute this value of y back into the equation we obtained for x:
x = -7 - 3y
x = -7 - 3(-4.7778)
x = -7 + 14.3334
x = 7.3334 (rounded to four decimal places)
So, the solution to the system of equations is x = 7.3334 and y = -4.7778 (rounded to four decimal places).
Part B
Note: Determine whether the solution to the new equation is a solution to the old system of equations by graphing. Use Desmos!
(1 point)
The solution to the original system of equations
A. is also
B. is not
a solution to the new equation.
Question 3
Solve the system of equations by SUBSTITUTION.
6y+5x=8
x+3y=−7
(1 point)
What would your equation look like after the first substitution
A. 6y+5(3y-7)=8
B. 6y+5(-3y-7)=8
C. 6(-3y-7)+5x=8
D. 6(3y-7)+5x=-7
To determine whether the solution to the new equation is a solution to the old system of equations, we can graph the original system of equations and see if the solution point lies on the graph.
Using Desmos, if we graph the original system of equations:
Equation 1: 6y + 5x = 8
Equation 2: x + 3y = -7
The point of intersection of the two lines on the graph will represent the solution to the system of equations. If the solution to the new equation lies on this point of intersection, then it is a solution to the old system of equations.
Regarding the first substitution:
6y + 5(3y-7) = 8
A is the correct choice because it represents the substitution of (3y-7) for x in the original equation 6y + 5x = 8.
C and D are incorrect choices because they do not represent the substitution of (3y-7) for x. B is also incorrect because it represents the substitution of (-3y-7) for x, which is not the case.
So the equation after the first substitution would be:
6y + 5(3y-7) = 8 (Choice A)
To determine whether the solution to this equation is a solution to the old system of equations, we need to evaluate the point of intersection on the graph.