Final answer:
To solve the system of equations using substitution, first express one equation in terms of a single variable. Then equate the expressions for y and solve for x. Finally, substitute the solution for x into either of the original equations to solve for y.
Step-by-step explanation:
To solve the system of equations using substitution, start by expressing one equation in terms of a single variable. We can take the equation y = 3x - 8 and solve for y to get y = -4x + 13. Now we have two equations:
y = 3x - 8
y = -4x + 13
Since both equations are solved for y, we can equate the expressions for y and solve for x. Setting 3x - 8 equal to -4x + 13, we have:
3x - 8 = -4x + 13
Combine like terms:
7x = 21
Divide both sides by 7:
x = 3
Substitute the value of x back into either of the original equations to solve for y. Using y = 3x - 8, we have:
y = 3(3) - 8
y = 9 - 8
y = 1
So the solution to the system of equations is x = 3 and y = 1.