The first step in solving this system of equations is to remove either the \(\displaystyle x\) term or the \(\displaystyle y\) term. This is done by multiplying the second equation by \(\displaystyle -1\).

\(\displaystyle -1(4x + 2y) = 8 (-1)\)

\(\displaystyle -4x - 2y = -8\)

Now add these two equations together and the \(\displaystyle y\) terms will be removed. 

     \(\displaystyle 8x + 2y = 4\)

+ \(\displaystyle -4x - 2y =- 8\)

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       \(\displaystyle 4x = -4\)

Divide both sides of the equation by \(\displaystyle 4.\)

\(\displaystyle x = -1\)

Put the value of \(\displaystyle x\), which is \(\displaystyle -1\), into one of the equations to get the value of \(\displaystyle y.\)

\(\displaystyle -8 + 2y = 4\)

Add \(\displaystyle 8\) to both sides of the equation.

\(\displaystyle 2y = 12\)

Divide both sides by \(\displaystyle 2.\)

\(\displaystyle y = 6\)

\(\displaystyle (-1,6)\) is the correct answer.

To solve this system of equations, add. This will eliminate or remove the \(\displaystyle x\) terms.

     \(\displaystyle 3x + y = 11\)

+\(\displaystyle -3x + y = 9\)

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             \(\displaystyle 2y = 20\)

Divide both sides by \(\displaystyle 2.\)

\(\displaystyle y = 10\)

To get the value of \(\displaystyle x,\) replace the variable with the value of that variable in one of the equations.

\(\displaystyle 3x + 10 = 11\)

Subtract \(\displaystyle 10\) from both sides of the equation.

\(\displaystyle 3x + 10 - 10 = 11-10\)

\(\displaystyle 3x = 1\)

Divide both sides of the equation by \(\displaystyle 3.\)

\(\displaystyle x = \frac{1}{3}\)

\(\displaystyle (\frac{1}{3},10)\) is the correct answer.

\(\displaystyle 5x -2y = 25\)

\(\displaystyle 4x-2y=24\)

To solve this system of equations,  subtract the second equation from the first.

       \(\displaystyle 5x - 2y = 25\)

     \(\displaystyle -4x + 2y = -24\)

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                   \(\displaystyle x=1\)

Now, substitute in the value for x into one of the equations to solve for the value of \(\displaystyle y\).

\(\displaystyle \\5x-2y = 25 \\5(1)-2y=25 \\5-2y=25\)

Now subtract five from each side.

\(\displaystyle \\5-5-2y=25-5 \\-2y=20\)

Divide both sides by negative 2:

\(\displaystyle \\ \frac{-2y}{-2}=\frac{20}{-2} \\ \\y=-10\)

\(\displaystyle x = 1\)

\(\displaystyle (1,-10)\) is the correct answer.

To solve this system of equations, set both equations equal to one another.

\(\displaystyle \frac{1}{5}x +2 = -\frac{1}{5}x-4\)

Add \(\displaystyle \frac{1}{5}x\) to both sides of the equation.

\(\displaystyle \frac{1}{5}x + \frac{1}{5}x + 2= -\frac{1}{5}x +\frac{1}{5}x -4\)

\(\displaystyle \frac{2}{5}x + 2 = -4\)

Subtract \(\displaystyle 2\) from both sides of the equation.

\(\displaystyle \frac{2}{5}x + 2 -2 = -4-2\)

\(\displaystyle \frac{2}{5}x =-6\)

Multiply both sides of the equation by \(\displaystyle \frac{5}{2}\).

\(\displaystyle \frac{2}{5}x \times \frac{5}{2} = \frac{-6}{1} \times \frac{5}{2}\)

\(\displaystyle x = \frac{-30}{2}\)

\(\displaystyle x = -15\)

Plug the value of \(\displaystyle x\), which is \(\displaystyle -15\) into one of the equations to get the value of \(\displaystyle y.\)

\(\displaystyle -\frac{1}{5 }\times \frac{-15}{1 } - 4 = y\)

\(\displaystyle 3-4 = y\)

\(\displaystyle y = -1\)

\(\displaystyle (-15,-1)\)  is the correct answer for this system of equations. 

Step 1: Write the two equations, one below another and line up the terms.

\(\displaystyle x-y=5\)
\(\displaystyle x+y=7\)
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Step 2: We see that we have \(\displaystyle -y\) and \(\displaystyle y\). We can add these two equations up, which will isolate y and let us solve for x.

\(\displaystyle x{\color{Red} -y}=5\)
\(\displaystyle x+{\color{Blue} y}=7\) We add here.
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\(\displaystyle 2x=12\)

Step 3: We will isolate x by itself. We need to divide by 2 on both sides to get x.

\(\displaystyle \frac {2x}{2}=\frac {12}{2}\)
\(\displaystyle \rightarrow x=6\)

Step 4: We found x, so we can plug in that value into any one of the two equations and solve for y. Let's choose equation (1).

(1)...\(\displaystyle x-y=5\)
\(\displaystyle (6)-y=5\). Isolate y by itself. We are going to subtract 6 from both sides.
\(\displaystyle 6-6-y=5-6\). Simplify the left hand side.
\(\displaystyle -y=-1\)

Step 5: We will divide by -1 to get the value of y.

\(\displaystyle \frac {-y}{-1}=\frac {-1}{-1}\)
\(\displaystyle \rightarrow y=1\)

The values that solve this system of equations is \(\displaystyle x=6\) and \(\displaystyle y=1\).

To answer this question you must first solve for one of the variables. This can be done with either variable with either equation. In this example of how to solve the problem we will solve for y using the second equation

\(\displaystyle 8x+4y=12\)

subtract 8x from both sides

\(\displaystyle 4y=12-8x\)

divide both sides by y

\(\displaystyle y=3-2x\)

Now we plug this into the first equation for the y variable

\(\displaystyle 4x+3(3-2x)=11\)

Distribute the 3

\(\displaystyle 4x+9-6x=11\)

Simplify

\(\displaystyle -2x+9=11\)

subtract 9 from both sides

\(\displaystyle -2x=2\)

divide by -2 on both sides

\(\displaystyle x=-1\)

Using this we solve for y in the second equation

\(\displaystyle 8(-1) +4y=12\)

simplify

\(\displaystyle -8+4y=12\)

add 8 to both sides

\(\displaystyle 4y=20\)

divide by 4 on both sides

\(\displaystyle y=5\)

Final answer\(\displaystyle x=-1\) and \(\displaystyle y=5\)