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sweet-ann [11.9K]
3 years ago
13

How to solve systems of equations: 4x+5y=11

Mathematics
2 answers:
Mariana [72]3 years ago
8 0
<span><span><span><span><span><span>4x+5y = 11 and 2x+6y = 16
</span>Let's start by solving 4x+5y = 11 for the variable x.
<span>Move the 5y to the right hand side by subtracting 5y from both sides, like this:
</span><span>From the left hand side:
<span>5y - 5y = 0
</span></span><span>The answer is 4x
</span></span><span>From the right hand side:
<span>The answer is 11-5y</span></span><span>
Now, the equation reads:
4x = 11-5y 
To isolate the x, we have to divide both sides of the equation by theother 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 4 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>4x ÷ 4 = x
</span><span>To divide 11-5y by 4</span><span>divide each term in 11-5y by 4 term by term.</span><span>11 ÷ 4 =11/4
</span><span>To divide y by 1
</span><span>The y just gets copied along in the numerator.</span></span><span>-5y ÷ 4 =</span><span>The solution to your equation is:
x =</span><span><span>Next, let's solve 2x+6y = 16 for the variable y.
<span>Move the 2x to the right hand side by subtracting 2x from both sides, like this:
</span><span>From the left hand side:
<span>2x - 2x = 0</span></span><span>The answer is 6y</span></span><span>From the right hand side:
<span>The answer is 16-2x</span></span><span>
Now, the equation reads:
6y = 16-2x 
To isolate the y, we have to divide both sides of the equation by theother variables
around the y on the left side of the equation.
</span><span>The last step is to divide both sides of the equation by 6 like this:
<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>6y ÷ 6 = y</span><span>To divide 16-2x by 6</span><span>divide each term in 16-2x by 6 term by term.</span><span>16 ÷ 6 =</span><span>To divide x by 1</span><span>The x just gets copied along in the numerator.</span></span><span>-2x ÷ 6 =</span><span>The solution to your equation is:
y =</span><span>Now, plug the earlier result, x=11/4-5/4y, in for x everywhere it occurs in 
y=8/3-1/3x.
This gives y=8/3-1/3(11/4-5/4y). Now all we have to do is solve this for y,to have our first solution.
<span><span>8/3 evaluates to </span><span>1/3 evaluates to </span><span>11/4 evaluates to </span><span>5/4 evaluates to </span><span>Multiply y and</span><span>Multiply y and 1</span><span>The y just gets copied along.</span><span>The answer is y</span>y<span>5/4*y evaluates to </span><span>11/4-5/4*y evaluates to </span><span>Multiply by</span><span>we multiply by each term in term by term.</span>This is the distributive property of multiplication.<span>Multiply and</span>1<span> × =</span><span>Multiply and</span><span>Multiply 1 and y</span><span>The y just gets copied along.</span>y<span> × =</span><span>1/3*(11/4-5/4*y) evaluates to </span><span> - =</span><span>The answer is</span><span>8/3-1/3*(11/4-5/4*y) evaluates to </span><span>Move the to the left hand side by subtracting from both sides, like this:
From the left hand side:
<span>y - =</span></span><span>The answer is</span><span>From the right hand side:
<span> - = 0</span></span><span>The answer is</span><span>
Now, the equation reads:
 = 
To isolate the y, we have to divide both sides of the equation by theother variables
around the y on the left side of the equation.
</span><span>The last step is to divide both sides of the equation by like this:
<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</span><span> ÷ = 3</span><span>The solution to your equation is:
y = 3</span><span>Lastly, to find the solution for x, we plug this answer for y into the earlier result that
x=11/4-5/4y.
This gives x=11/4-5/4(3). Now, simplify this.
<span><span>11/4 evaluates to </span><span>5/4 evaluates to </span><span>Multiply and 3</span>1<span>5/4*(3) evaluates to </span><span>11/4-5/4*(3) evaluates to -1</span><span>x= -1</span><span>So, the solutions to your equations are:
x= -1 and y= 3</span></span></span></span></span></span></span><span>The answer is x</span></span><span>The answer is y</span>
</span></span></span>
Anastasy [175]3 years ago
5 0
4x+5y=11
2x+6y=16

2x=16-6y
x=8-3y

4(8-3y)+5y=11
32-12y+5y=11
-7y=-21
y=3

4x+5(3)=11
4x+15=11
4x=-4
x=-1
(-1,3)
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