Question

Use the substitution method to solve the system of equations.

2x – 5y = –14
x – 2y = –5

Answer 1

x=3 y=4

Answer 2

Equation 1: 2x-5y = -14
Equation 2: x-2y = -5
You can solve for x or y using either equation 1 or 2.
I'll solve for x using Equation 2:
Step 1: Solve for x (means you want x=something)
Equation 2: x-2y= -5
x=-5+2y (Added 2y to both left and right hand sides)
Step 2: Substitute x=-5+2y into Equation 1 and solve for y
Equation 1: 2x-5y =-14
2(-5+2y) -5y=-14 substitute x=-5+2y
-10+4y-5y=-14 Distribute the 2
-10-y=-14 Simplify
-y=-14+10 Added 10 to both sides
-y=-4 Simplify
y=4 Divide both sides by -1
Step 3: Using y=4 plug this back into Equation 1 or Equation 2 and solve for x (now you'll get x= a number)
Equation 2: x-2y=-5
x-2(4)=-5 Substitute y=4
x-8=-5 simplify
x=-5+8 added 8 to both sides
x=3 simplify
So your solution is x=3 and y=4 or another way to state this is (3,4) is a solution of the system of equations. Another way to say this is, the lines given by Equation 1 and Equation 2 intersect at the point (3,4)