Solve the system of equations. {:[-5y+4x=49],[7y+2x=-23],[x=◻],[y=◻]:}

Identify Variable to Eliminate: Identify the variable to eliminate. We can choose to eliminate either 'x' or 'y' by multiplying the equations by appropriate numbers so that the coefficients of one variable will be opposites.Multiply Equations by Appropriate Numbers: Multiply the first equation by 7 and the second equation by -5 to get the coefficients of 'y' to be opposites. 7(-5y + 4x) = 7(49) -5(7y + 2x) = -5(-23) This gives us: -35y + 28x = 343 -35y - 10x = 115Add Equations to Eliminate 'y': Add the equations to eliminate 'y'. (-35y + 28x) + (-35y - 10x) = 343 + 115 -35y + 28x - 35y - 10x = 458 -70y + 18x = 458Correct Calculation: There seems to be a mistake in the previous step. The coefficients of 'y' are the same, so they should cancel out when added. Let's correct the calculation. -35y + 28x - 35y - 10x = 343 + 115 -70y + 18x = 458 This is incorrect. The correct calculation should be: -35y + 28x + 35y - 10x = 343 + 115 28x - 10x = 458 18x = 458

Resources

Testimonials

Plans

Resources

Testimonials

Plans

AI tutor

Welcome to Bytelearn!

Let’s check out your problem:

Solve the system of equations.

{:[-5y+4x=49],[7y+2x=-23],[x=◻],[y=◻]:}

Solve the system of equations. $\newline$ $-5 y+4 x=49$ $\newline$ $7 y+2 x=-23$ $\newline$ $x=$ $\newline$ $y=$

View step-by-step help

Home

Math Problems

Algebra 2

Solve a system of equations using elimination

Full solution

Q. Solve the system of equations.

\newline

-5 y+4 x=49

\newline

7 y+2 x=-23

\newline

x=

\newline

y=

Identify Variable to Eliminate: Identify the variable to eliminate. We can choose to eliminate either ' $x$ ' or ' $y$ ' by multiplying the equations by appropriate numbers so that the coefficients of one variable will be opposites.
Multiply Equations by Appropriate Numbers: Multiply the first equation by $7$ and the second equation by $-5$ to get the coefficients of 'y' to be opposites. $\newline$ $7(-5y + 4x) = 7(49)$ $\newline$ $-5(7y + 2x) = -5(-23)$ $\newline$ This gives us: $\newline$ $-35y + 28x = 343$ $\newline$ $-35y - 10x = 115$
Add Equations to Eliminate 'y': Add the equations to eliminate 'y'. $\newline$ $(-35y + 28x) + (-35y - 10x) = 343 + 115$ $\newline$ $-35y + 28x - 35y - 10x = 458$ $\newline$ $-70y + 18x = 458$
Correct Calculation: There seems to be a mistake in the previous step. The coefficients of 'y' are the same, so they should cancel out when added. Let's correct the calculation. $\newline$ $-35y + 28x - 35y - 10x = 343 + 115$ $\newline$ $-70y + 18x = 458$ $\newline$ This is incorrect. The correct calculation should be: $\newline$ $-35y + 28x + 35y - 10x = 343 + 115$ $\newline$ $28x - 10x = 458$ $\newline$ $18x = 458$