Solving Equations Using Substitution Quick Check
1 of 51 of 5 Items
Question
Solve the system of two equations using substitution.
y=2+3x
4x−3y=−16 (1 point)
To solve the system of equations using substitution, we can substitute the expression for y from the first equation into the second equation.
Given:
y = 2 + 3x
4x - 3y = -16
Substitute y = 2 + 3x into the second equation:
4x - 3(2 + 3x) = -16
4x - 6 - 9x = -16
-5x - 6 = -16
-5x = -10
x = 2
Now that we have found the value of x, we can substitute it back into the first equation to find the value of y:
y = 2 + 3(2)
y = 2 + 6
y = 8
Therefore, the solution to the system of equations is x = 2, y = 8.
The solution to the system of equations using substitution is:
x = 2
y = 8
Therefore, the answer is x = 2, y = 8.
To solve the system of equations, we can use substitution or elimination. Let's use substitution in this case.
Given equations:
2x + 6y = -18
x = 5y - 1
Substitute x = 5y - 1 into the first equation:
2(5y - 1) + 6y = -18
10y - 2 + 6y = -18
16y - 2 = -18
16y = -16
y = -1
Now that we have found the value of y, we can substitute it back into the second equation to find the value of x:
x = 5(-1) - 1
x = -5 - 1
x = -6
Therefore, the solution to the system of equations is:
x = -6
y = -1
To solve the system of equations, we can use the elimination method. Let's eliminate one of the variables by adding or subtracting the equations.
Given equations:
3x + y = 2
7x - 4y = 30
First, let's multiply the first equation by 4 to make the y coefficients opposite in sign:
4(3x + y) = 4(2)
12x + 4y = 8
Now, we can add the modified first equation to the second equation to eliminate y:
12x + 4y + 7x - 4y = 8 + 30
19x = 38
x = 2
Now that we have found the value of x, we can substitute it back into the first equation to find the value of y:
3(2) + y = 2
6 + y = 2
y = -4
Therefore, the solution to the system of equations is:
x = 2
y = -4
To solve the system of equations, we can use the elimination method. Let's eliminate one of the variables by adding or subtracting the equations.
Given equations:
-4x + 6y = 38
x - 5y = -20
First, let's multiply the second equation by 4 to make the x coefficients opposite in sign:
4(x - 5y) = 4(-20)
4x - 20y = -80
Now, we can add the equations to eliminate x:
-4x + 6y + 4x - 20y = 38 - 80
-14y = -42
y = 3
Now that we have found the value of y, we can substitute it back into the second equation to find the value of x:
x - 5(3) = -20
x - 15 = -20
x = -5
Therefore, the solution to the system of equations is:
x = -5
y = 3
To determine the number of solutions that the system of equations has, we can use the elimination method. Let's eliminate one of the variables by adding or subtracting the equations.
Given equations:
-5x + y = -18
10x - 2y = 36
First, let's multiply the first equation by 2 to make the y coefficients opposite in sign:
2(-5x + y) = 2(-18)
-10x + 2y = -36
Now, we can add both equations to eliminate y:
-10x + 2y + 10x - 2y = -36 + 36
0 = 0
Since 0 = 0, this system of equations has an infinite number of solutions. The two equations are actually the same when multiplied by constants, which means they are linearly dependent and there are infinitely many points that satisfy both equations.
so what is the answer
Question
Solve the system of equations.
2x+6y=−18
x=5y−1 (1 point)
Solve the system of equations.
3x+y=2
7x−4y=30 (1 point)
Solve the system of equations.
−4x+6y=38
x−5y=−20 (1 point)