The problem to solve is:
The goal here is to solve
y=-2x-7 and
y=-3x-9 for the variables y and x.
<span>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.
<span>Multiply x and 2</span><span>Multiply x and 1</span><span>The x just gets copied along.</span><span>The answer is x</span>x<span>2*x evaluates to 2x</span>Because of the minus sign<span>2x becomes - 2x</span><span>The answer is -2x</span><span>-2*x-7 evaluates to -2x-7</span><span>So, all-in-all, your first equation can be written as: y = -2x-7</span><span>Now, let's work on your second equation,y=-3x-9<span> <span>Multiply x and 3</span></span><span>Multiply x and 1</span><span>The x just gets copied along.</span><span>The answer is x</span>x<span>3*x evaluates to 3x</span>Because of the minus sign<span>3x becomes - 3x</span><span>The answer is -3x</span><span>-3*x-9 evaluates to -3x-9</span><span>So, all-in-all, your second equation can be written as: y = -3x-9</span><span><span>After this initial survey of the equations, the system of equations we'll set out to solve is:
<span>y = -2x-7 and y = -3x-9</span>Let'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:
<span>y - y = 0</span><span>The answer is 0</span></span><span>From the right hand side:
<span>The answer is -3x-9-y</span></span><span>
Now, the equation reads:
0 = -3x-9-y</span></span><span>Move the -3x to the left hand side by adding 3x to both sides, like this:
To the left hand side:
<span>The answer is 3x</span></span><span>To the right hand side:
<span>-3x + 3x = 0x</span></span><span>The answer is -9-y</span><span>
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.
</span><span>The last step is to divide both sides of the equation by 3 like this:
<span>To divide x by 1</span><span>The x just gets copied along in the numerator.</span><span>The answer is x</span><span>3x ÷ 3 = x</span><span>To divide -9-y by 3</span><span>divide each term in -9-y by 3 term by term.</span><span>-9 ÷ 3 = -3</span><span>To divide y by 1</span><span>The y just gets copied along in the numerator.</span><span>The answer is y</span><span>-y ÷ 3 =</span><span>The solution to your equation is:
x =</span><span>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.
<span>Because of the minus sign3 becomes - 3<span>The answer is -3</span><span>1/3 evaluates to </span><span>Multiply x and 2</span><span>Multiply x and 1</span><span>The x just gets copied along.</span><span>The answer is x</span>x<span>2*x evaluates to 2x</span>Because of the minus sign<span>2x becomes - 2x</span><span>The answer is -2x</span><span>-2*x-7 evaluates to -2x-7</span><span>Multiply by -2x-7</span><span>we multiply by each term in -2x-7 term by term.</span>This is the distributive property of multiplication.<span>Multiply and -2x</span><span>Multiply 1 and x</span><span>The x just gets copied along.</span>x<span> × -2x =</span><span>Multiply and -7</span>1<span> × -7 =</span><span>1/3*(-2*x-7) evaluates to </span><span>-3 - =</span>The answer is<span>-3-1/3*(-2*x-7) evaluates to </span><span>Move the to the left hand side by subtracting from both sides, like this:
From the left hand side:
<span>x - =</span></span>The answer is<span>From the right hand side:
<span> - = 0</span></span>The answer is<span>
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.
</span><span><span><span><span>The last step is to divide both sides of the equation by like this:
<span>To divide x by 1</span><span>The x just gets copied along in the numerator.</span><span>The answer is x</span><span> ÷ = x</span><span> ÷ = -2</span><span>The solution to your equation is:
x = -2</span><span><span>Lastly, 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.
<span>Because of the minus sign2 becomes - 2<span>The answer is -2</span></span></span><span>2 becomes - 2</span></span></span><span>Multiply -2 and -2</span>1<span>-2*(-2) evaluates to 4</span><span>-2*(-2)-7 evaluates to -3</span><span>y= -3</span><span>So, the solutions to your equations are:
y= -3 and x= -2</span></span>Because of the minus sign</span><span>The answer is -2</span><span>
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