Math / Algebra

Question12. Use the elimination method by subtraction to solve for $x$ and $y$ .
Equation $1 \quad 4 x-3 y=-4$ Equation $2 \quad 4 x+5 y=28$
12a First solve for $y$ . Enter your next step here $12 b$ Submit step

Studdy Solution

STEP 1

What is this asking? We're asked to find the values of $x$ and $y$ that satisfy both equations, using the elimination method specifically by subtracting the equations. Watch out! Be super careful with signs when subtracting equations!
It's easy to make a mistake there.

STEP 2

1. Eliminate $x$
2. Solve for $y$
3. Substitute and solve for $x$

STEP 3

Notice that both equations have the same $4x$ term.
This is perfect for elimination by subtraction!

STEP 4

$(4x + 5y) - (4x - 3y) = 28 - (-4)$ Why are we doing this?
Because subtracting the equations will eliminate the $x$ variable, leaving us with an equation only in terms of $y$ , which we can then solve!

STEP 5

$4x + 5y - 4x + 3y = 28 + 4$ $(4x - 4x) + (5y + 3y) = 32$ $0 + 8y = 32$ $8y = 32$ We've successfully eliminated $x$ !

STEP 6

To isolate $y$ , we'll divide both sides of the equation by 8. $\frac{8y}{8} = \frac{32}{8}$ Why divide by 8?
Because it's the coefficient of $y$ , and dividing by it turns $8y$ into $1 \cdot y$ , which is just $y$ !

STEP 7

$y = \textbf{4}$ Yay, we found the value of $y$ !

STEP 8

Now, let's substitute our shiny new value of $y = \textbf{4}$ back into Equation 1: $4x - 3y = -4$ . $4x - 3(\textbf{4}) = -4$ Why are we doing this?
We want to find the value of $x$ , and now that we know $y$ , we can plug it into either of our original equations to solve for $x$ !

STEP 9

$4x - 12 = -4$

STEP 10

Add 12 to both sides of the equation: $4x - 12 + 12 = -4 + 12$ $4x = 8$ Now, divide both sides by 4: $\frac{4x}{4} = \frac{8}{4}$

STEP 11

$x = \textbf{2}$ We did it!
We found the value of $x$ !

STEP 12

The solution to the system of equations is $x = \textbf{2}$ and $y = \textbf{4}$ .

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Question12. Use the elimination method by subtraction to solve for $x$ and $y$ .
Equation $1 \quad 4 x-3 y=-4$ Equation $2 \quad 4 x+5 y=28$
12a First solve for $y$ . Enter your next step here $12 b$ Submit step

Studdy Solution

STEP 1

What is this asking? We're asked to find the values of $x$ and $y$ that satisfy both equations, using the elimination method specifically by subtracting the equations. Watch out! Be super careful with signs when subtracting equations!
It's easy to make a mistake there.

STEP 2

1. Eliminate $x$
2. Solve for $y$
3. Substitute and solve for $x$

STEP 3

Notice that both equations have the same $4x$ term.
This is perfect for elimination by subtraction!

STEP 4

$(4x + 5y) - (4x - 3y) = 28 - (-4)$ Why are we doing this?
Because subtracting the equations will eliminate the $x$ variable, leaving us with an equation only in terms of $y$ , which we can then solve!

STEP 5

$4x + 5y - 4x + 3y = 28 + 4$ $(4x - 4x) + (5y + 3y) = 32$ $0 + 8y = 32$ $8y = 32$ We've successfully eliminated $x$ !

STEP 6

To isolate $y$ , we'll divide both sides of the equation by 8. $\frac{8y}{8} = \frac{32}{8}$ Why divide by 8?
Because it's the coefficient of $y$ , and dividing by it turns $8y$ into $1 \cdot y$ , which is just $y$ !

STEP 7

$y = \textbf{4}$ Yay, we found the value of $y$ !

STEP 8

Now, let's substitute our shiny new value of $y = \textbf{4}$ back into Equation 1: $4x - 3y = -4$ . $4x - 3(\textbf{4}) = -4$ Why are we doing this?
We want to find the value of $x$ , and now that we know $y$ , we can plug it into either of our original equations to solve for $x$ !

STEP 9

$4x - 12 = -4$

STEP 10

Add 12 to both sides of the equation: $4x - 12 + 12 = -4 + 12$ $4x = 8$ Now, divide both sides by 4: $\frac{4x}{4} = \frac{8}{4}$

STEP 11

$x = \textbf{2}$ We did it!
We found the value of $x$ !

STEP 12

The solution to the system of equations is $x = \textbf{2}$ and $y = \textbf{4}$ .

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Question12. Use the elimination method by subtraction to solve for xxx and yyy.Equation 14x−3y=−41 \quad 4 x-3 y=-414x−3y=−4 Equation 24x+5y=282 \quad 4 x+5 y=2824x+5y=2812a First solve for yyy. Enter your next step here 12b12 b12b Submit step

Studdy Solution

STEP 1

What is this asking? We're asked to find the values of xxx and yyy that satisfy both equations, using the elimination method specifically by subtracting the equations. Watch out! Be super careful with signs when subtracting equations!It's easy to make a mistake there.

STEP 2

1. Eliminate xxx2. Solve for yyy3. Substitute and solve for xxx

STEP 3

Notice that both equations have the same 4x4x4x term.This is perfect for elimination by subtraction!

STEP 4

(4x+5y)−(4x−3y)=28−(−4)(4x + 5y) - (4x - 3y) = 28 - (-4)(4x+5y)−(4x−3y)=28−(−4) Why are we doing this?Because subtracting the equations will eliminate the xxx variable, leaving us with an equation only in terms of yyy, which we can then solve!

STEP 5

4x+5y−4x+3y=28+44x + 5y - 4x + 3y = 28 + 44x+5y−4x+3y=28+4 (4x−4x)+(5y+3y)=32(4x - 4x) + (5y + 3y) = 32(4x−4x)+(5y+3y)=32 0+8y=320 + 8y = 320+8y=328y=328y = 328y=32We've successfully eliminated xxx!

STEP 6

To isolate yyy, we'll divide both sides of the equation by **8**. 8y8=328 \frac{8y}{8} = \frac{32}{8} 88y​=832​ Why divide by 8?Because it's the coefficient of yyy, and dividing by it turns 8y8y8y into 1⋅y1 \cdot y1⋅y, which is just yyy!

STEP 7

y=4 y = \textbf{4} y=4 Yay, we found the value of yyy!

STEP 8

STEP 9

4x−12=−4 4x - 12 = -4 4x−12=−4

STEP 10

Add **12** to both sides of the equation: 4x−12+12=−4+12 4x - 12 + 12 = -4 + 12 4x−12+12=−4+12 4x=8 4x = 8 4x=8Now, divide both sides by **4**: 4x4=84 \frac{4x}{4} = \frac{8}{4} 44x​=48​

STEP 11

x=2 x = \textbf{2} x=2 We did it!We found the value of xxx!

STEP 12

The solution to the system of equations is x=2x = \textbf{2}x=2 and y=4y = \textbf{4}y=4.

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Question12. Use the elimination method by subtraction to solve for $x$ and $y$ .
Equation $1 \quad 4 x-3 y=-4$ Equation $2 \quad 4 x+5 y=28$
12a First solve for $y$ . Enter your next step here $12 b$ Submit step

What is this asking? We're asked to find the values of $x$ and $y$ that satisfy both equations, using the elimination method specifically by subtracting the equations. Watch out! Be super careful with signs when subtracting equations!
It's easy to make a mistake there.

1. Eliminate $x$
2. Solve for $y$
3. Substitute and solve for $x$

Notice that both equations have the same $4x$ term.
This is perfect for elimination by subtraction!

$(4x + 5y) - (4x - 3y) = 28 - (-4)$ Why are we doing this?
Because subtracting the equations will eliminate the $x$ variable, leaving us with an equation only in terms of $y$ , which we can then solve!

$4x + 5y - 4x + 3y = 28 + 4$ $(4x - 4x) + (5y + 3y) = 32$ $0 + 8y = 32$ $8y = 32$ We've successfully eliminated $x$ !

To isolate $y$ , we'll divide both sides of the equation by 8. $\frac{8y}{8} = \frac{32}{8}$ Why divide by 8?
Because it's the coefficient of $y$ , and dividing by it turns $8y$ into $1 \cdot y$ , which is just $y$ !

$y = \textbf{4}$ Yay, we found the value of $y$ !

$4x - 12 = -4$

Add 12 to both sides of the equation: $4x - 12 + 12 = -4 + 12$ $4x = 8$ Now, divide both sides by 4: $\frac{4x}{4} = \frac{8}{4}$

$x = \textbf{2}$ We did it!
We found the value of $x$ !

The solution to the system of equations is $x = \textbf{2}$ and $y = \textbf{4}$ .