1. Gina wrote this system of linear equations:
2x + y = 7
4x + 5y = 11
Which of the following shows the first four steps that Gina could have used to correctly solve this system for x?
a) y = 7 – 2x
4x + 5(7 – 2x) = 11
4x + 25 – 10x = 11
25 – 6x = 11
b) y = 7 – 2x
4x + 5(7 – 2x) = 11
4x + 35 – 10x = 11
35 – 6x = 11
c) y = 7 – 2x
4x + 5 + (7 – 2x) = 11
2x + 12 = 11
2x = 12 – 11
d) x = 11 – 5y
4x + 5(11 – 5y) = 11
4x + 55 – 10x = 11
4x + 10x = 55 + 11
Answer = b.
The correct answer is a) y = 7 - 2x
To solve this system of linear equations, we need to use one of the elimination methods, such as substitution or elimination.
Step 1: Rearrange the first equation to solve for y.
2x + y = 7
y = 7 - 2x
Step 2: Substitute the value of y into the second equation.
4x + 5(7 - 2x) = 11
Step 3: Distribute the 5 to terms inside the parentheses.
4x + 35 - 10x = 11
Step 4: Combine like terms.
-6x + 35 = 11
So the correct answer is a) y = 7 - 2x
4x + 5(7 - 2x) = 11
4x + 35 - 10x = 11