1. What is the solution to the system of equations below?
3x - 2y = 7
4x + 5y = 1
To solve this system of equations, we can use either substitution or elimination method.
Let's use elimination method:
Multiply the first equation by 5 and the second equation by 2 to make the coefficient of y the same:
15x - 10y = 35
8x + 10y = 2
Add the two equations together:
23x = 37
x = 37/23
x = 1.6
Substitute x back into one of the equations to solve for y:
3(1.6) - 2y = 7
4.8 - 2y = 7
-2y = 2.2
y = -1.1
Therefore, the solution to the system of equations is x = 1.6 and y = -1.1.
2. What is the most common error when solving a system of equations using the elimination method?
The most common error when solving a system of equations using the elimination method is making a mistake when adding or subtracting the equations to eliminate one of the variables. It is important to be careful with signs and coefficients when performing this step, as an error can lead to an incorrect solution.
3. How many solutions can a system of linear equations have?
A system of linear equations can have one solution, no solution, or infinitely many solutions, depending on the relationship between the equations. If the equations represent parallel lines, they will have no solution. If the equations represent the same line, they will have infinitely many solutions. If the equations intersect at a single point, they will have one solution.
Algebra 1 unit 4 lesson 3 quick check
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