Solve the following system of equations using substitution: y = 3x + 2, y = 4x - 7. What is the value of y?
Linear equations are equations that have a degree of one. They are useful in calculations. They have at most one root, that is, they can cut the x-axis only once but not necessarily. They also have a constant slope at each point.
Answer: The solution to the system of equations given is (9, 29) in the form of (x, y). The value of y is 29.
Let's understand how we arrived at the solution.
⇒ y = 3x + 2
⇒ y = 4x - 7
Let's use the substitution method to solve this.
Now, we substitute the values of y from the second equation into the first equation.
⇒ (4x - 7) = 3x + 2
⇒ 4x - 3x = 2 + 7
⇒ x = 9
Now, putting the value of x into the second equation:
⇒ y = 4(9) - 7 = 36 - 7 = 29
We can arrive at the same result by putting x = 9 in the first equation.
Hence, The solution to the system of equations given is (9, 29) in the form of (x, y). The value of y is 29.