Question

y = 3x + 3 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.

Answer 1

Y = 3x + 3
y = x - 1

As you can see, both equations are set to equal y. This means the right sides of each equation are equal, since y is isolated in both equations. So to solve this particular system of equations for x, set the right sides of both equations equal to each other. After you've done that, you can proceed to solve the equation algebraically for the variable, x.

3x + 3 = x - 1
2x + 3 = -1
2x = -4
x = -2

Negative two is the x-value. To find the y-value, substitute -2 for x into either equation and solve algebraically for y.

y = x - 1
y = -2 - 1
y = -3

The final step is to check all work by plugging both x- and y-values back into both equations.

y = 3x + 3
-3 = 3(-2) + 3
-3 = -6 + 3
-3 = -3  --  This is true

y = x - 1
-3 = -2 - 1
-3 = -3  --  This is true.

Answer:
(-2, -3)