The problem to solve is:
The goal here is to solve
y=-2x-7 and
y=-3x-9 for the variables y and x.
First, let's work on your first equation,y=-2x-7This means, see if it can be simplified at all before attempting to solve it.
Multiply x and 2Multiply x and 1The x just gets copied along.The answer is xx2*x evaluates to 2xBecause of the minus sign2x becomes - 2xThe answer is -2x-2*x-7 evaluates to -2x-7So, all-in-all, your first equation can be written as: y = -2x-7Now, let's work on your second equation,y=-3x-9 Multiply x and 3Multiply x and 1The x just gets copied along.The answer is xx3*x evaluates to 3xBecause of the minus sign3x becomes - 3xThe answer is -3x-3*x-9 evaluates to -3x-9So, all-in-all, your second equation can be written as: y = -3x-9After this initial survey of the equations, the system of equations we'll set out to solve is:
y = -2x-7 and y = -3x-9Let's start by solving y = -2x-7 for the variable y.
To isolate the y, we have to divide both sides of the equation by the other variables
around the y on the left side of the equation.
and this is the final solution to your equation.Next, let's solve y = -3x-9 for the variable x.
Move the y to the right hand side by subtracting y from both sides, like this:
From the left hand side:
y - y = 0The answer is 0From the right hand side:
The answer is -3x-9-y
Now, the equation reads:
0 = -3x-9-yMove the -3x to the left hand side by adding 3x to both sides, like this:
To the left hand side:
The answer is 3xTo the right hand side:
-3x + 3x = 0xThe answer is -9-y
Now, the equation reads:
3x = -9-y
To isolate the x, we have to divide both sides of the equation by the other variables
around the x on the left side of the equation.
The last step is to divide both sides of the equation by 3 like this:
To divide x by 1The x just gets copied along in the numerator.The answer is x3x ÷ 3 = xTo divide -9-y by 3divide each term in -9-y by 3 term by term.-9 ÷ 3 = -3To divide y by 1The y just gets copied along in the numerator.The answer is y-y ÷ 3 =The solution to your equation is:
x =Now, plug the earlier result, y=-2x-7, in for y everywhere it occurs in
x=-3-1/3y.
This gives x=-3-1/3(-2x-7). Now all we have to do is solve this for x,to have our first solution.
Because of the minus sign3 becomes - 3The answer is -31/3 evaluates to Multiply x and 2Multiply x and 1The x just gets copied along.The answer is xx2*x evaluates to 2xBecause of the minus sign2x becomes - 2xThe answer is -2x-2*x-7 evaluates to -2x-7Multiply by -2x-7we multiply by each term in -2x-7 term by term.This is the distributive property of multiplication.Multiply and -2xMultiply 1 and xThe x just gets copied along.x × -2x =Multiply and -71 × -7 =1/3*(-2*x-7) evaluates to -3 - =The answer is-3-1/3*(-2*x-7) evaluates to Move the to the left hand side by subtracting from both sides, like this:
From the left hand side:
x - =The answer isFrom the right hand side:
- = 0The answer is
Now, the equation reads:
=
To isolate the x, we have to divide both sides of the equation by the other variables
around the x on the left side of the equation.
The last step is to divide both sides of the equation by like this:
To divide x by 1The x just gets copied along in the numerator.The answer is x ÷ = x ÷ = -2The solution to your equation is:
x = -2Lastly, to find the solution for y, we plug this answer for x into the earlier result that
y=-2x-7.
This gives y=-2(-2)-7. Now, simplify this.
Because of the minus sign2 becomes - 2The answer is -22 becomes - 2Multiply -2 and -21-2*(-2) evaluates to 4-2*(-2)-7 evaluates to -3y= -3So, the solutions to your equations are:
y= -3 and x= -2Because of the minus signThe answer is -2
