Explain how to solve this system of two equations.
x+2y=4 and x-2y=6
Fill in the blanks using:
system of equations
equivalent
like terms
collecting like terms
combining like terms
evaluate
substitution method
elimination method
distributive property
inverse operation
parallel
perpendicular
collinear
coincident
solution
no solution
infinitely many solution
inconsistent equation
Jabari had two equations to solve. Both had two unknowns, x and y. Jabari could use them to solve each other. That's called (_______). Jabari decided to (_______) using the substitution method. First, he had to turn the x's in one equation into y's. He subtracted 2y from both sides of the first equation x+2y = 4. This made x = 4−2y.
Next, he substituted the expression 4−2y for x in (_______). Now he had (4-2y)−2y = 6.
Jabari saw that the two 2y's were like terms. He knew that collecting like terms is a way to (_______). He combined the y's to get 4−4y = 6.
From there, he subtracted 4 from both sides to get −4y=2. Now it was easy to evaluate the expression down to a single value. The problem's solution was (_______).