Consider the following pair of equations:
y = −2x + 8
y = x − 1
Explain how you will solve the pair of equations by substitution. Show all the steps and write the solution in (x, y) form. (5 points)
To solve the pair of equations using substitution, we first need to solve one of the equations for one of the variables, and then substitute that expression into the other equation.
Given equations are:
y = −2x + 8
y = x − 1
Let's solve the second equation for y:
y = x − 1
Now, we substitute this expression for y in the first equation:
−2x + 8 = x − 1
Next, we isolate x by moving x to one side and constants to the other side:
−2x - x = -1 - 8
-3x = -9
x = 3
Now that we have x, we can substitute it back into one of the original equations to solve for y. Let's use the first equation:
y = -2(3) + 8
y = -6 + 8
y = 2
Therefore, the solution to the pair of equations in (x, y) form is:
x = 3, y = 2