{2x−y=9} {2x+7y=17}

{2x−y=9} {2x+7y=17}

Systems of equations
asked 2021-02-06
\(\displaystyle{\left\lbrace{2}{x}−{y}={9}\right\rbrace}\) \(\displaystyle{\left\lbrace{2}{x}+{7}{y}={17}\right\rbrace}\)

Answers (1)

To solve a system of equations, you should use the substitution method or the elimination method. The substitution method should be used if one of the equations has a variable that can be easily solved for. The elimination method should be used if the equations have a variable term with the same or opposite coefficients or if neither equation can be easily solved for a variable.
The first equation can be easily solved for yy but the equations have the same coefficient for the xx terms so the elimination method will be easier to use.
To use the elimination method, subtract the two equations to eliminate the xx terms. Then solve for y:
Now that you the value of y, substitute it into either equation and then solve for x:
The solution of the system is then (x,y)=(5,1).

Relevant Questions

asked 2021-02-12
Manuel has $54 to buy CDs and books. Each CD costs $9, and each book costs $6. He wants to buy exactly 7 items to spend all of his money. Write a system of equations that could be solved to determine the number of CDs and the number of books Manuel buys.
asked 2021-05-18
When \(2x^{2}-7+9\) is divided by a polynomial, the quotient is 2x - 3 and the remainder is 3. Find the polynomial?
asked 2021-05-19
Consider the function \(f(x)=2x^{3}-6x^{2}-18x+9\) on the interval [-2,4].
What is the absolute minimum of f(x) on [-2,4]?
What is the absolute maximum of f(x) on [-2,4]?
asked 2021-05-07
Find \(\displaystyle{\frac{{{\left.{d}{y}\right.}}}{{{\left.{d}{x}\right.}}}}\) using the rules for finding derivatives.
asked 2021-03-23
Solve the system of equations.
asked 2021-02-01

Point K is on line segment \(\overline{JL}\). Given \(JK = 2x - 2, KL = x - 9,\ and\ JL = 2x + 8,\) determine the numerical length of \(\overline{KL}\).

asked 2021-05-30
Verify the factorization using the FOIL method.
asked 2021-05-17
Use the Differentiation Formulas and Rules of Derivatives to find the derivatives of the following functions.
asked 2021-03-22
Solve the system of equations x+y=-1 and 5x-7y=79 by combining the equations.
asked 2021-02-20
Find the first partial derivatives.