Substitution
Pick either equation, and solve for either variable.
What is the first step in solving by substitution?
pick a variable to modify to be the same value as in the other equation.
What is the first step in solving with Elimination?
plot your y-intercept, then use slope to find your next points.
How do we graph slope intercept form?
because the process is easier for each type of solving method.
Why is there a specific way that works best for each System of Equation?
Infinite, One and Zero
What are the solutions to a System of Equations?
To replace a piece with something else.
What does it mean to substitute?
multiplication or division, one or both equations.
How do we modify the values to match?
solve each part, x - ? and y - ?, and then combine to make one point. Then use slope to find the next points.
How do we graph point slope form?
our own choice.
What dictates/decides how we solve an equation?
One where the slope intercept and the slope are equal, the solution is equal and the lines on a graph are the same.
What is an Infinite Solution?
The variable with a coefficient of 1.
Which is the best variable to pick to solve for?
multiply each by their counterpart.
What is the fastest way to modify coefficients to match?
Ignore/equal to zero each variable in turn and solve for the other variable. These are your x and y intercepts respectfully, plot them and connect with a line.
How do you graph standard form?
the setup of the equations
how do we know which way to solve the system of equations?
One in which the answer doesn't make sense, the slope is the same, the y-intercept is different and the lines are parallel.
What is a Zero Solution?
How many times do we substitute when solving by substitution?
When the matched values are opposite. One positive, one negative.
When do you add the like terms in the equations?
Dashed versus solid line, shading above/below lines and knowing multiplying/dividing by a negative will flip the inequality.
The value of the coefficients
What is the thing we look at to know whether to substitute or eliminate?
One in which there is an answer for y or x, the slope is different and the y-intercept doesn't matter and the lines intersect.
What is One Solution?
We still isolate the variable and then have to divide by the coefficient.
How do we solve for a variable when there isn't a coefficient of 1?
When the matched values are equal. Both positive or negative.
When do you subtract the like terms in the equations?
Standard form because the coefficients can throw off the intercepts and make the dots not be exact.
Which is the least effective equation to graph?
Be able to identify the best method to solve the system of equation, explain why and solve it using that method.
How do you get Advanced one this topic?
Solving multi-step equations.
What is the most important skill for solving System of Equations?