solve
{y=x-7
{5x+2y=7
Use the substitution method.
A.(0, −7)
B.(7, 0)
C.(3, −4)
D.(−1, −8)
so, substitute y=x-7 into
5x+2y = 7
5x+2(x-7) = 7
...
soo b
stop guessing. Next step:
5x+2x-14 = 7
...
B works for the 1st equation, but not the second.
To solve this system of equations using the substitution method, we will solve one equation for one variable and substitute it into the other equation. Let's start:
1. Given equations:
y = x - 7 --------(Equation 1)
5x + 2y = 7 --------(Equation 2)
2. Solve Equation 1 for y:
y = x - 7
3. Substitute the value of y from Equation 1 into Equation 2:
5x + 2(x - 7) = 7
4. Simplify and solve for x:
5x + 2x - 14 = 7
7x - 14 = 7
7x = 21
x = 3
5. Substitute the value of x into Equation 1 to find y:
y = 3 - 7
y = -4
6. Therefore, the solution to the system of equations is (x, y) = (3, -4).
Now, let's check the options given:
A. (0, -7):
Equation 1: y = x - 7
Equation 2: 5x + 2y = 7
If we substitute (0, -7) into both equations, we get:
Equation 1: -7 = 0 - 7 ==> -7 = -7 (True)
Equation 2: 5(0) + 2(-7) = 7 ==> -14 = 7 (False)
B. (7, 0):
Equation 1: y = x - 7
Equation 2: 5x + 2y = 7
If we substitute (7, 0) into both equations, we get:
Equation 1: 0 = 7 - 7 ==> 0 = 0 (True)
Equation 2: 5(7) + 2(0) = 7 ==> 35 = 7 (False)
C. (3, -4):
Equation 1: y = x - 7
Equation 2: 5x + 2y = 7
If we substitute (3, -4) into both equations, we get:
Equation 1: -4 = 3 - 7 ==> -4 = -4 (True)
Equation 2: 5(3) + 2(-4) = 7 ==> 15 - 8 = 7 ==> 7 = 7 (True)
D. (-1, -8):
Equation 1: y = x - 7
Equation 2: 5x + 2y = 7
If we substitute (-1, -8) into both equations, we get:
Equation 1: -8 = -1 - 7 ==> -8 = -8 (True)
Equation 2: 5(-1) + 2(-8) = 7 ==> -5 - 16 = 7 ==> -21 = 7 (False)
Based on the calculations, we can see that the only option that satisfies both equations is C. (3, -4).