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7x+10 y=60
7x-2y=240
If (x,y) satisfies the given system of equations, what is the value of x?

◻

$7x+10y=60$ $\newline$ $7x-2y=240$ $\newline$ If $(x,y)$ satisfies the given system of equations, what is the value of $x$ ? $\newline$ ◻

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Write an equation word problem

Full solution

Q.

7x+10y=60

\newline

7x-2y=240

\newline

If

(x,y)

satisfies the given system of equations, what is the value of

x

?

\newline

◻

Stack Equations: First, let's stack the equations to see them clearly: $\newline$ $1$ ) $7x + 10y = 60$ $\newline$ $2$ ) $7x - 2y = 240$
Eliminate x: Now, we'll subtract the second equation from the first to eliminate x: $\newline$ $(7x + 10y) - (7x - 2y) = 60 - 240$
Simplify Equation: This simplifies to: $10y + 2y = -180$
Combine Like Terms: Combine like terms: $12y = -180$
Solve for y: Now, divide both sides by $12$ to solve for y: $\newline$ $y = \frac{-180}{12}$
Substitute into Equation: Calculating the value of $y$ : $y = -15$
Isolate $7x$ Term: Now that we have the value of $y$ , we can substitute it back into one of the original equations to solve for $x$ . Let's use the first equation: $\newline$ $7x + 10(-15) = 60$
Solve for x: Simplify the equation: $7x - 150 = 60$
Calculate Value of x: Add $150$ to both sides to isolate the $7x$ term: $\newline$ $7x = 60 + 150$
Calculate Value of x: Add $150$ to both sides to isolate the $7x$ term: $\newline$ $7x = 60 + 150$ Calculate the sum: $\newline$ $7x = 210$
Calculate Value of x: Add $150$ to both sides to isolate the $7x$ term: $\newline$ $7x = 60 + 150$ Calculate the sum: $\newline$ $7x = 210$ Finally, divide both sides by $7$ to solve for $x$ : $\newline$ $x = 210 / 7$
Calculate Value of x: Add $150$ to both sides to isolate the $7x$ term: $\newline$ $7x = 60 + 150$ Calculate the sum: $\newline$ $7x = 210$ Finally, divide both sides by $7$ to solve for $x$ : $\newline$ $x = 210 / 7$ Calculate the value of $x$ : $\newline$ $x = 30$

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