Solve the system of equations. {:[5x+12 y-10=0],[2x-3y+35=0],[x=◻],[y=◻]:}

Write equations: Write down the system of equations to be solved. We have the following system of equations: 5x + 12y - 10 = 0 2x - 3y + 35 = 0Solve for x: Solve the first equation for x. We can rearrange the first equation to express x in terms of y: 5x + 12y - 10 = 0 5x = 10 - 12y x = (10 - 12y) / 5Substitute x into second equation: Substitute the expression for x from Step 2 into the second equation. Substituting x = (10 - 12y) / 5 into 2x - 3y + 35 = 0 gives us: 2((10 - 12y) / 5) - 3y + 35 = 0 Multiplying through by 5 to clear the fraction: 2(10 - 12y) - 15y + 175 = 0 20 - 24y - 15y + 175 = 0Combine terms and solve for y: Combine like terms and solve for y. 20 - 24y - 15y + 175 = 0 -39y + 195 = 0 -39y = -195 y = -195 / -39 y = 5Substitute y into x expression: Substitute the value of y back into the expression for x from Step 2. Substituting y = 5 into x = (10 - 12y) / 5 gives us: x = (10 - 12(5)) / 5 x = (10 - 60) / 5 x = -50 / 5 x = -10Write solution as ordered pair: Write the solution as an ordered pair. The solution to the system of equations is (x, y) = (-10, 5).

Resources

Testimonials

Plans

Resources

Testimonials

Plans

AI tutor

Welcome to Bytelearn!

Let’s check out your problem:

Solve the system of equations.

{:[5x+12 y-10=0],[2x-3y+35=0],[x=◻],[y=◻]:}

Solve the system of equations. $\newline$ $\begin{array}{l} 5 x+12 y-10=0 \\ 2 x-3 y+35=0 \\ x=\square \\ y=\square \end{array}$

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

\begin{array}{l} 5 x+12 y-10=0 \\ 2 x-3 y+35=0 \\ x=\square \\ y=\square \end{array}

Write equations: Write down the system of equations to be solved. $\newline$ We have the following system of equations: $\newline$ $5x + 12y - 10 = 0$ $\newline$ $2x - 3y + 35 = 0$
Solve for x: Solve the first equation for x. $\newline$ We can rearrange the first equation to express x in terms of y: $\newline$ $5x + 12y - 10 = 0$ $\newline$ $5x = 10 - 12y$ $\newline$ $x = \frac{10 - 12y}{5}$
Substitute $x$ into second equation: Substitute the expression for $x$ from Step $2$ into the second equation. $\newline$ Substituting $x = \frac{10 - 12y}{5}$ into $2x - 3y + 35 = 0$ gives us: $\newline$ $2\left(\frac{10 - 12y}{5}\right) - 3y + 35 = 0$ $\newline$ Multiplying through by $5$ to clear the fraction: $\newline$ $2(10 - 12y) - 15y + 175 = 0$ $\newline$ $20 - 24y - 15y + 175 = 0$
Combine terms and solve for $y$ : Combine like terms and solve for $y$ . $\newline$ $20 - 24y - 15y + 175 = 0$ $\newline$ $-39y + 195 = 0$ $\newline$ $-39y = -195$ $\newline$ $y = \frac{-195}{-39}$ $\newline$ $y = 5$
Substitute $y$ into $x$ expression: Substitute the value of $y$ back into the expression for $x$ from Step $2$ . $\newline$ Substituting $y = 5$ into $x = \frac{10 - 12y}{5}$ gives us: $\newline$ $x = \frac{10 - 12(5)}{5}$ $\newline$ $x = \frac{10 - 60}{5}$ $\newline$ $x = \frac{-50}{5}$ $\newline$ $x = -10$
Write solution as ordered pair: Write the solution as an ordered pair. $\newline$ The solution to the system of equations is $(x, y) = (-10, 5)$ .