We read your photo as:

Solve the system of linear equations: 2x − 3y = 5 and 3x − 2y = 20.

Mathematics

ScanSolve AI Answer

Answer

x=10,y=5x=10, y=5

Step-by-step solution

5 steps

  1. Multiply the first equation by 2 and the second equation by 3 to make the coefficients of yy equal.

    The given system of equations is:

    2x−3y=5(1)2x - 3y = 5 \quad \text{(1)} 3x−2y=20(2)3x - 2y = 20 \quad \text{(2)}

    Multiply equation (1) by 2:

    2(2x−3y)=2(5)2(2x - 3y) = 2(5) 4x−6y=10(3)4x - 6y = 10 \quad \text{(3)}

    Multiply equation (2) by 3:

    3(3x−2y)=3(20)3(3x - 2y) = 3(20) 9x−6y=60(4)9x - 6y = 60 \quad \text{(4)}

  2. Subtract equation (3) from equation (4) to eliminate yy.

    (9x−6y)−(4x−6y)=60−10(9x - 6y) - (4x - 6y) = 60 - 10 9x−6y−4x+6y=509x - 6y - 4x + 6y = 50 5x=505x = 50

  3. Solve for xx.

    x=505x = \frac{50}{5} x=10x = 10

  4. Substitute the value of xx into equation (1) to solve for yy.

    2(10)−3y=52(10) - 3y = 5 20−3y=520 - 3y = 5

  5. Solve for yy.

    −3y=5−20-3y = 5 - 20 −3y=−15-3y = -15 y=−15−3y = \frac{-15}{-3} y=5y = 5

    The solution to the system of equations is:

    x=10,y=5x=10, y=5
Was this helpful?

Try one yourself

A new problem that tests the same skill.

Still stuck on this one?

Ask a follow-up, and the answer starts from this question.

Got a different question?Ask your own question

More Mathematics Questions

QSolve the system of linear equations: 2x + 2y = 10 and 3x − y = 3.QSolve the following system of linear equations: 3x − 4y = 5 and 9x + y = 4.QSolve the system of equations: 2x + y = 3 and 4x − 2y = 4.
Browse by topic:Algebra
See all Mathematics questions →
Got a syllabus? Photograph it and I'll tell you what's due and what's worth the most.
Handwritten step-by-step solution preview

Handwritten Step-by-Step Solution

Get this as a handwritten image on WhatsApp — like a tutor wrote it for you.

Try on WhatsApp