How would you solve this systems of equations?
Y-7=-2x
4x+2y=14
the system has no unique solution
the equations are equivalent...you can make them the same by manipulation
... multiply 1st eqn by 2
... add 4x + 7 to both sides
... you now have the 2nd eqn
Eq1: Y = -2x + 7. m = -2.
Eq2: 4x + 2y = 14. m = -A/B = -4/2 = -2.
The Eqs have equal slopes and do not intersect. Therefore, there is no solution.
Henry is correct about the slopes being equal
he didn't mention, but the intercepts are also equal
the lines are the same
... there are an infinite number of solutions
if you know the value of one variable, you know the other
To solve the system of equations:
1. Start by isolating the variable with a coefficient of 1 in one of the equations. Let's focus on the first equation.
Given: Y - 7 = -2x
We can isolate Y by adding 7 on both sides: Y = -2x + 7
2. Now, substitute the expression for Y in the second equation, as we have Y isolated.
Given: 4x + 2y = 14
Substitute Y = -2x + 7 into the second equation: 4x + 2(-2x + 7) = 14
3. Simplify and solve for x.
Distribute 2 to -2x and 7: 4x - 4x + 14 = 14
Combine like terms: 14 = 14
Since the equation simplifies to 14 = 14, it means that both sides are equal, regardless of the value of x. This indicates that the two equations represent the same line and are dependent, meaning there are infinitely many solutions.
Therefore, the solution to the system of equations is all values of x and y that satisfy the equation Y = -2x + 7.