Answer:
5x + 2y = 7
3x � y = 2
multiply the second equation by 2 and leave the first equation as is to get:
5x + 2y = 7
6x � 2y = 4
add the second equation to the first equation to get:
11x = 11
divide both sides of that equation by 11 to get:
x = 1
replace x with 11 in the first original equation to get:
5x + 2y = 7 becomes 5 + 2y = 7
solve for y to get y = 1
your solution is x = 1 and y = 1
confirm by replacing x and y with 1 and 1 in both original equations to get:
5x + 2y = 7 becomes 5 + 2 = 7 which is true.
3x � y = 2 becomes 3 - 1 = 2 which is true.
Explanation:
Given a system of two equations in two variables, replacing one equation by the sum of that equation and a multiple of the other produces a system with the same solution. Show why this is true by solving the system of equations given. Justify the reason for each step. HINT: Use addition property of equality and multiplication property of equality in your answers.
5x + 2y = 7
3x � y = 2
A1. To solve the system using elimination, first multiply the bottom equation by 2. Write the new system of equations.
B1. Why is this multiplication allowed?
C1. What variable will be eliminated when the equations are combined after the multiplication?
D1. Next, add the equations together. Your answer should be a single equation with one variable.
E1. Why can you add the equations?
F1. Solve the equation for x.
G1. Substitute x back into one of the equations to solve for y.
H1. What is the solution to the system of equations?
I hope this helps! ο(=•ω＜=)ρ⌒☆