Solve the following system of equations:
–2x + 2y = 8
2x – 7y = 7
A. (–2, 2)
B. (–7, –3)
C. (1, 5)
D. (0, –1)
Solve the following system of equations:
4y + 2x = 14
2y + 2x = 10
A. (1, 4)
B. (3, 2)
C. (–7, 12)
D. (0, 7)
#1. Add the two equations to get
-5y = 15
#2. Subtract the two equations to get
2y = 4
To solve the first system of equations:
Step 1: Let's eliminate x by adding the two equations.
(-2x + 2y) + (2x - 7y) = 8 + 7
-2x + 2x + 2y - 7y = 15
-5y = 15
Step 2: Divide both sides of the equation by -5 to solve for y.
-5y / -5 = 15 / -5
y = -3
Step 3: Substitute the value of y back into one of the original equations to solve for x.
-2x + 2(-3) = 8
-2x - 6 = 8
-2x = 8 + 6
-2x = 14
x = 14 / -2
x = -7
Therefore, the solution to the first system of equations is (-7, -3), so the correct answer is option B.
To solve the second system of equations:
Step 1: Let's eliminate x by subtracting the second equation from the first equation.
(4y + 2x) - (2y + 2x) = 14 - 10
4y + 2x - 2y - 2x = 4
2y = 4
Step 2: Divide both sides of the equation by 2 to solve for y.
2y / 2 = 4 / 2
y = 2
Step 3: Substitute the value of y back into one of the original equations to solve for x.
4(2) + 2x = 14
8 + 2x = 14
2x = 14 - 8
2x = 6
x = 6 / 2
x = 3
Therefore, the solution to the second system of equations is (3, 2), so the correct answer is option B.
To solve a system of equations, we can use either the substitution method or the elimination method. Let's solve the first system of equations using the elimination method.
1) –2x + 2y = 8
2) 2x – 7y = 7
To eliminate the variable x, we can add equation 1 to equation 2. This will give us:
-2x + 2y + 2x - 7y = 8 + 7
Simplifying the equation:
-5y = 15
Now, we can solve for y by dividing both sides of the equation by -5:
y = -3
Once we have the value of y, we can substitute it back into one of the original equations to solve for x. Let's use equation 1:
-2x + 2(-3) = 8
Simplifying the equation:
-2x - 6 = 8
-2x = 14
x = -7
Therefore, the solution to the first system of equations is (-7, -3). Therefore, the correct answer choice is B.
Now, let's solve the second system of equations using the substitution method.
1) 4y + 2x = 14
2) 2y + 2x = 10
We can solve equation 2 for y:
2y = 10 - 2x
y = 5 - x
Now, we can substitute this value of y into equation 1:
4(5 - x) + 2x = 14
20 - 4x + 2x = 14
-2x = -6
x = 3
Once we have the value of x, we can substitute it back into the equation for y:
y = 5 - 3
y = 2
Therefore, the solution to the second system of equations is (3, 2). Therefore, the correct answer choice is B.