Math / Algebra

QuestionFind the solution to the system of equations. You can use the interactive graph below to find the solution. $\begin{array}{l} \left\{\begin{array}{l} 8 x-4 y=16 \\ 8 x+4 y=16 \end{array}\right. \\ x=\square \\ y=\square \end{array}$

Studdy Solution

STEP 1

What is this asking? We've got two equations with $x$ and $y$ , and we need to find the values of $x$ and $y$ that make both equations true! Watch out! Don't mix up your $x$ s and $y$ s, and be super careful with positive and negative signs during calculations.

STEP 2

1. Simplify the equations
2. Solve for $x$
3. Solve for $y$

STEP 3

Let's look at our equations: $8x - 4y = 16$ $8x + 4y = 16$ We can make these simpler by dividing everything in the first equation by 4: $\frac{8x}{4} - \frac{4y}{4} = \frac{16}{4}$ This simplifies to: $2x - y = 4$ Now, let's do the same for the second equation, dividing everything by 4: $\frac{8x}{4} + \frac{4y}{4} = \frac{16}{4}$ Which simplifies to: $2x + y = 4$ Much nicer, right?

STEP 4

Now, check this out!
We can add our two simplified equations together: $(2x - y) + (2x + y) = 4 + 4$ $2x - y + 2x + y = 8$ Notice how the $-y$ and $y$ add to zero, leaving us with: $4x = 8$ Now, divide both sides by 4 to get $x$ by itself: $\frac{4x}{4} = \frac{8}{4}$ $x = 2$ Awesome! We found $x$ !

STEP 5

Let's use the value of $x$ we just found ( $x = 2$ ) and plug it back into one of our simplified equations.
Let's use $2x + y = 4$ : $2 \cdot 2 + y = 4$ $4 + y = 4$ To get $y$ by itself, let's subtract 4 from both sides: $4 + y - 4 = 4 - 4$ $y = 0$ We did it!
We found both $x$ and $y$ !

STEP 6

$x = 2$ and $y = 0$ .
So the solution to the system of equations is $(2, 0)$ .

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QuestionFind the solution to the system of equations. You can use the interactive graph below to find the solution. $\begin{array}{l} \left\{\begin{array}{l} 8 x-4 y=16 \\ 8 x+4 y=16 \end{array}\right. \\ x=\square \\ y=\square \end{array}$

Studdy Solution

STEP 1

What is this asking? We've got two equations with $x$ and $y$ , and we need to find the values of $x$ and $y$ that make both equations true! Watch out! Don't mix up your $x$ s and $y$ s, and be super careful with positive and negative signs during calculations.

STEP 2

1. Simplify the equations
2. Solve for $x$
3. Solve for $y$

STEP 3

STEP 4

Now, check this out!
We can add our two simplified equations together: $(2x - y) + (2x + y) = 4 + 4$ $2x - y + 2x + y = 8$ Notice how the $-y$ and $y$ add to zero, leaving us with: $4x = 8$ Now, divide both sides by 4 to get $x$ by itself: $\frac{4x}{4} = \frac{8}{4}$ $x = 2$ Awesome! We found $x$ !

STEP 5

Let's use the value of $x$ we just found ( $x = 2$ ) and plug it back into one of our simplified equations.
Let's use $2x + y = 4$ : $2 \cdot 2 + y = 4$ $4 + y = 4$ To get $y$ by itself, let's subtract 4 from both sides: $4 + y - 4 = 4 - 4$ $y = 0$ We did it!
We found both $x$ and $y$ !

STEP 6

$x = 2$ and $y = 0$ .
So the solution to the system of equations is $(2, 0)$ .

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Studdy Solution

STEP 1

What is this asking? We've got two equations with xxx and yyy, and we need to find the values of xxx and yyy that make *both* equations true! Watch out! Don't mix up your xxxs and yyys, and be super careful with positive and negative signs during calculations.

STEP 2

1. Simplify the equations2. Solve for xxx3. Solve for yyy

STEP 3

STEP 4

STEP 5

STEP 6

x=2x = 2x=2 and y=0y = 0y=0.So the solution to the system of equations is (2,0)(2, 0)(2,0).

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Studdy solves anything!

Start learning now

Download Studdy AI Tutor now. Learn with ease and get all help you need to be successful at school.

What is this asking? We've got two equations with $x$ and $y$ , and we need to find the values of $x$ and $y$ that make both equations true! Watch out! Don't mix up your $x$ s and $y$ s, and be super careful with positive and negative signs during calculations.

1. Simplify the equations
2. Solve for $x$
3. Solve for $y$

$x = 2$ and $y = 0$ .
So the solution to the system of equations is $(2, 0)$ .