Solve using the substitution method. If the system has no solution or an infinite number of solutions, state this.
-2x + 0y = -14
x + 11y = 18
easiest and most obvious way:
from the first:
-2x = -14
x = 7
plug into the second
7 + 11y = 18
11y = 11
y = 1
To solve the system of equations using the substitution method, we need to isolate one variable in one of the equations and substitute its value into the other equation.
Let's begin solving the system.
1. Start with the first equation: -2x + 0y = -14.
Since the coefficient of y is 0, we can see that this equation does not involve y. Simplifying further, we have:
-2x = -14
2. Solve for x:
Divide both sides of the equation by -2:
x = -14 / -2
x = 7
So, we have found the value of x.
3. Substitute the value of x into the second equation: x + 11y = 18.
We found that x = 7, so we can replace x with 7:
7 + 11y = 18
4. Solve for y:
Subtract 7 from both sides of the equation:
11y = 18 - 7
11y = 11
Divide both sides of the equation by 11:
y = 11 / 11
y = 1
So, we have found the value of y.
5. Conclusion:
The solution to the system of equations is x = 7 and y = 1.