Question 1 Given the following system of equations, will it be easier to use substitution or elimination? What is the ordered pair that satisfies both equations? 3x + y = 40 and 4x + 2y = 58
To determine whether it will be easier to use substitution or elimination, we can analyze the coefficients of the variables in both equations.
In this case, it may be easier to use elimination because the coefficients of y in both equations are already the same (1 and 2) and can be easily eliminated by adding or subtracting the two equations.
To solve this system using elimination:
- Multiply the first equation by 2 to make the coefficients of y match: 6x + 2y = 80
- Subtract the second equation from this new equation: (6x + 2y) - (4x + 2y) = 80 - 58
- Simplify: 6x + 2y - 4x - 2y = 22
- Combine like terms: 2x = 22
- Divide both sides by 2: x = 11
Now substitute this value of x into one of the original equations to find the value of y:
3(11) + y = 40
33 + y = 40
Subtract 33 from both sides: y = 7
Therefore, the ordered pair (x, y) that satisfies both equations is (11, 7).