Question

Solve the system of equations by the substitution method: y = 2x + 7 and y = 9x - 8. What is the solution?

a) (1, 9)
b) (2, 15)
c) (3, 17)
d) (4, 23)

Answer 1

To solve the given system of linear equations by the substitution method, we substitute the expression for y from one equation into the other equation and solve for the remaining variable. The solution to the system is (15/7, 79/7) or approximately (2.14, 11.29).

Step-by-step explanation:

To solve the system of equations using the substitution method, we need to solve one of the equations for one variable and substitute that expression into the other equation. Let's solve y = 2x + 7 for y:

Since y is already isolated in this equation, we can substitute it into the second equation:

2x + 7 = 9x - 8

Next, we solve for x:

7 + 8 = 9x - 2x

15 = 7x

x = 15/7

Now that we have the value of x, we can substitute it back into the first equation to find y:

y = 2(15/7) + 7

y = 30/7 + 49/7

y = 79/7

Therefore, the solution to the system of equations is (15/7, 79/7), which can be approximate to (2.14, 11.29).