Math  /  Algebra

QuestionSolve:- 4x+2y=10xy=13\begin{array}{l} 4 x+2 y=10 \\ x-y=13 \end{array}

Studdy Solution

STEP 1

1. We have a system of two linear equations with two variables x x and y y .
2. The goal is to find the values of x x and y y that satisfy both equations simultaneously.
3. We can use either the substitution method or the elimination method to solve the system.

STEP 2

1. Choose a method to solve the system of equations.
2. Solve for one variable.
3. Substitute the expression into the other equation.
4. Solve for the second variable.
5. Substitute back to find the first variable.
6. Verify the solution by plugging the values back into the original equations.

STEP 3

Let's use the substitution method for this problem.

STEP 4

Solve the second equation for x x :
xy=13 x - y = 13
Add y y to both sides:
x=y+13 x = y + 13

STEP 5

Substitute x=y+13 x = y + 13 into the first equation:
4(y+13)+2y=10 4(y + 13) + 2y = 10

STEP 6

Distribute and simplify the equation:
4y+52+2y=10 4y + 52 + 2y = 10
Combine like terms:
6y+52=10 6y + 52 = 10
Subtract 52 from both sides:
6y=42 6y = -42
Divide by 6:
y=7 y = -7

STEP 7

Substitute y=7 y = -7 back into the expression for x x :
x=7+13 x = -7 + 13
Simplify:
x=6 x = 6

STEP 8

Verify the solution by substituting x=6 x = 6 and y=7 y = -7 back into the original equations:
First equation:
4(6)+2(7)=10 4(6) + 2(-7) = 10
2414=10 24 - 14 = 10
True.
Second equation:
6(7)=13 6 - (-7) = 13
6+7=13 6 + 7 = 13
True.
Both equations are satisfied.
The solution is:
x=6,y=7 x = 6, \, y = -7

Was this helpful?

Studdy solves anything!

banner

Start learning now

Download Studdy AI Tutor now. Learn with ease and get all help you need to be successful at school.

ParentsInfluencer programContactPolicyTerms
TwitterInstagramFacebookTikTokDiscord