Solve the system of equations. 8x−3y= −22 y=10+4x (1 point)
We can solve this system of equations by substituting the value of y from the second equation into the first equation.
From the second equation, we have y = 10 + 4x.
Substituting this into the first equation:
8x - 3(10 + 4x) = -22.
Now, we can distribute the -3:
8x - 30 - 12x = -22.
Combining like terms, we have:
-4x - 30 = -22.
Adding 30 to both sides:
-4x = 8.
Dividing by -4:
x = -2.
Now that we have the value of x, we can substitute it back into the second equation to find y:
y = 10 + 4(-2).
Simplifying:
y = 10 - 8.
y = 2.
Therefore, the solution to the system of equations is x = -2 and y = 2.
Solve the system of equations. 5x+2y=14 x−6y=22 (1 point)
We can solve this system of equations using the method of elimination or substitution.
Let's use the method of elimination.
First, we multiply the second equation by 5 to match the coefficients of x:
5(x-6y) = 5(22)
5x - 30y = 110
Now, we can subtract the first equation from this new equation:
(5x - 30y) - (5x + 2y) = 110 - 14
Simplifying:
-30y - 2y = 110 - 14
-32y = 96
y = -3
Now, we can substitute the value of y back into one of the original equations. Let's use the first equation:
5x + 2(-3) = 14
5x - 6 = 14
5x = 20
x = 4
Therefore, the solution to the system of equations is x = 4 and y = -3.
Solve the system of equations. –9x+y=12 2x+4y= −28 (1 point)
We can solve this system of equations using the method of substitution.
First, isolate y in the first equation:
-9x + y = 12
y = 9x + 12
Now substitute this expression for y in the second equation:
2x + 4(9x + 12) = -28
Simplify:
2x + 36x + 48 = -28
Combine like terms:
38x + 48 = -28
Subtract 48 from both sides:
38x = -76
Divide by 38:
x = -2
Now substitute the value of x back into the expression for y:
y = 9(-2) + 12
y = -18 + 12
y = -6
Therefore, the solution to the system of equations is x = -2 and y = -6.
To solve the system of equations:
1. Start by substituting 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 on the left side:
-4x - 30 = -22
4. Add 30 to both sides of the equation:
-4x = -22 + 30
-4x = 8
5. Divide both sides of the equation by -4 to solve for x:
x = 8 / -4
x = -2
6. Now, substitute the value of x into the second equation:
y = 10 + 4(-2)
y = 10 - 8
y = 2
7. Therefore, the solution to the system of equations is x = -2 and y = 2.
To solve the system of equations, we will use the method of substitution. Here's how you can get the solution:
Step 1: Start with the given system of equations:
8x - 3y = -22 ...(Equation 1)
y = 10 + 4x ...(Equation 2)
Step 2: Solve Equation 2 for y by isolating it:
y = 10 + 4x
Step 3: Substitute the value of y from Equation 2 into Equation 1:
8x - 3(10 + 4x) = -22
Step 4: Distribute the -3 to simplify the equation:
8x - 30 - 12x = -22
Step 5: Combine like terms on the left-hand side:
(8x - 12x) - 30 = -22
-4x - 30 = -22
Step 6: Add 30 to both sides of the equation to isolate the variable:
-4x - 30 + 30 = -22 + 30
-4x = 8
Step 7: Divide both sides of the equation by -4 to solve for x:
-4x / -4 = 8 / -4
x = -2
Step 8: Now that we have the value of x, substitute it back into Equation 2 to find the value of y:
y = 10 + 4x
y = 10 + 4(-2)
y = 10 - 8
y = 2
So the solution to the system of equations is x = -2 and y = 2.