Home/Integrated Math 1/Lesson 77

Is (x, y) a solution to the system of equations?

Verify system solutions by checking both equations.

Do this: Read the concept below, then try the quiz or activity.

Lesson 77 of 192

40%

Concept

Objective: Students will verify candidate solutions to systems of equations.

Estimated Time: 12 minutes

Standards:

HSA-REI.C.6HSA-REI.D.10

A point solves a system only if it satisfies every equation in that system simultaneously.

Try it

Check if (2, 3) solves y = x + 1 and 2x + y = 7.

⚖️ System Solver (2x2)

Test candidate points against both equations in the system.

Equation 1

2x + 1y = 9

Equation 2

1x - 1y = 1

Determinant: D = ae - bd = (2)(-1) - (1)(1) = -3
x = (ce - bf) / D = (9-1 - 1+1) / -3 = 3.333
y = (af - cd) / D = (2+1 - 9+1) / -3 = 2.333

Solution: (3.333, 2.333)

Concept Check

A point that works in one equation but not the other is:

A system solution

Not a system solution

Always on both lines

Equivalent form

Concept Check

If two lines intersect at one point, the system has:

No solutions

One solution

Infinitely many

Undefined

Common Misconception

Always verify your result in context instead of trusting a first pass.

System check steps

These steps are out of order — can you fix them?

1.Substitute into equation 2

2.Substitute into equation 1

3.Evaluate truth values

4.Conclude yes/no

Short Answer

How is checking a system different from checking one equation?

Mastery Check

Pass this check with at least 80% to unlock completion.

Question 1