Solve using elimination. –7x + 3y = 14 –7x + 4y = 7 (_____, _____)

Set up equations: First, we need to set up the equations to eliminate one of the variables. We have the following system of equations: –7x + 3y = 14 –7x + 4y = 7Eliminate variable x: To eliminate the variable x, we can subtract the second equation from the first equation. This will give us an equation with only the variable y. (–7x + 3y) - (–7x + 4y) = 14 - 7Subtract equations: Perform the subtraction to find the equation in terms of y. –7x + 3y + 7x - 4y = 14 - 7Simplify equation: Simplify the equation by combining like terms. (–7x + 7x) + (3y - 4y) = 14 - 7 0x - y = 7Solve for y: Since 0x is 0, we can remove it from the equation, leaving us with: -y = 7Substitute y value: To solve for y, we need to multiply both sides of the equation by -1. y = -7Perform multiplication: 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: –7x + 3y = 14Isolate x term: Substitute y = -7 into the equation. –7x + 3(-7) = 14Simplify equation: Simplify the equation by performing the multiplication. –7x - 21 = 14Divide to solve x: Add 21 to both sides of the equation to isolate the term with x. –7x - 21 + 21 = 14 + 21Calculate x value: Simplify the equation. –7x = 35Divide both sides by -7 to solve for x. x = 35 / -7Calculate the value of x. x = -5

Resources

Testimonials

Plans

Resources

Testimonials

Plans

AI tutor

Welcome to Bytelearn!

Let’s check out your problem:

Solve using elimination. $\newline$ $-7x + 3y = 14$ $\newline$ $-7x + 4y = 7$ $\newline$ (_, _)

View step-by-step help

Home

Math Problems

Grade 8

Solve a system of equations using elimination

Full solution

Q. Solve using elimination.

\newline

-7x + 3y = 14

\newline

-7x + 4y = 7

\newline

(_____, _____)

Set up equations: First, we need to set up the equations to eliminate one of the variables. We have the following system of equations: $\newline$ $-7x + 3y = 14$ $\newline$ $-7x + 4y = 7$
Eliminate variable $x$ : To eliminate the variable $x$ , we can subtract the second equation from the first equation. This will give us an equation with only the variable $y$ . $(–7x + 3y) - (–7x + 4y) = 14 - 7$
Subtract equations: Perform the subtraction to find the equation in terms of $y$ . $-7x + 3y + 7x - 4y = 14 - 7$
Simplify equation: Simplify the equation by combining like terms. $\newline$ $(–7x + 7x) + (3y - 4y) = 14 - 7$ $\newline$ $0x - y = 7$
Solve for y: Since $0x$ is $0$ , we can remove it from the equation, leaving us with: $\newline$ $-y = 7$
Substitute y value: To solve for $y$ , we need to multiply both sides of the equation by $-1$ . $y = -7$
Perform multiplication: 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: $\newline$ $–7x + 3y = 14$
Isolate x term: Substitute $y = -7$ into the equation. $\,-7x + 3(-7) = 14$
Simplify equation: Simplify the equation by performing the multiplication. $-7x - 21 = 14$
Divide to solve $x$ : Add $21$ to both sides of the equation to isolate the term with $x$ . $\newline$ $-7x - 21 + 21 = 14 + 21$
Calculate $x$ value: Simplify the equation. $\,-7x = 35$
Calculate $x$ value: Simplify the equation. $-7x = 35$ Divide both sides by $-7$ to solve for $x$ . $x = \frac{35}{-7}$
Calculate $x$ value: Simplify the equation. $-7x = 35$ Divide both sides by $-7$ to solve for $x$ . $x = \frac{35}{-7}$ Calculate the value of $x$ . $x = -5$