Use substitution to solve the system of equations. y=4x+5𝑦=4𝑥+5 2x+y=17

Step 1: We have two equations here:

Equation 1: y = 4x + 5 Equation 2: 2x + y = 17

Step 2: We can substitute Equation 1 into Equation 2 because they both have 'y'. This means wherever we see 'y' in Equation 2, we can replace it with '4x + 5' from Equation 1.

So, Equation 2 becomes: 2x + (4x + 5) = 17

Step 3: Simplify the equation by combining like terms:

2x + 4x + 5 = 17 6x + 5 = 17

Step 4: Solve for 'x' by subtracting 5 from both sides of the equation:

6x = 17 - 5 6x = 12 x = 12 / 6 x = 2

Step 5: Now that we have 'x', we can substitute 'x' into Equation 1 to find 'y':

y = 4x + 5 y = 4(2) + 5 y = 8 + 5 y = 13

So, the solution to the system of equations is x = 2 and y = 13.