5x+y=7
6x+7y= -9
Solve for system of equations.
What is the solution?
Is it inconsistent or consistent?
Is it dependent or independent?
5x+y=7
6x+7y= -9
6x+7(7-5x)=-9
X=2
Y=-3
check answers by plugging into the equations
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To solve the system of equations:
Step 1: Simplify both equations if necessary.
The given equations are already in simplified form.
Step 2: Choose one equation and solve for one variable in terms of the other.
Let's solve the first equation for y:
5x + y = 7
y = 7 - 5x
Step 3: Substitute the expression obtained in Step 2 into the other equation.
Substituting y = 7 - 5x into the second equation:
6x + 7(7 - 5x) = -9
Step 4: Solve the equation obtained in Step 3 for the remaining variable.
6x + 49 - 35x = -9
-29x + 49 = -9
-29x = -58
x = 2
Step 5: Substitute the value of x back into either of the original equations to find the value of y.
Using the first equation:
5(2) + y = 7
10 + y = 7
y = -3
Therefore, the solution to the system of equations is x = 2 and y = -3.
To determine if the system is consistent or inconsistent, we need to check if the equations have any solution or no solution.
The given system of equations has a unique solution, so it is consistent.
To determine if the system is dependent or independent, we analyze the coefficients of the variables.
In this case, since the system has a unique solution (x,y) = (2, -3), the system is independent.