Final answer:
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).