Question

X + y = 7 2x - 3y = -21

Answer 1

Answer:

one solution

Step-by-step explanation:

Step: Solvex+y=7for x:

x+y+−y=7+−y(Add -y to both sides)

x=−y+7

Step: Substitute−y+7forxin2x−3y=−21:

2x−3y=−21

2(−y+7)−3y=−21

−5y+14=−21(Simplify both sides of the equation)

−5y+14+−14=−21+−14(Add -14 to both sides)

−5y=−35

−5y

−5

=

−35

−5

(Divide both sides by -5)

y=7

Step: Substitute 7 for y in x=−y+7:

x=−y+7

x=−7+7

x=0(Simplify both sides of the equation)

y = 7, x = 0

Answer 2

There is only one solution

When you graph both equations, they intersect therefore the intersection point tells you there is one solution. If it was infinitely many solutions then it would be the same line. If it was no solution then the graph would show to parallel lines.