Math / Algebra

Questionems of Iline ar equations by 7. $\begin{array}{l} 8 x-7 y=-3 \\ 6 x-5 y=-1 \end{array}$

Studdy Solution

STEP 1

What is this asking? We've got two equations with two mystery numbers, $x$ and $y$ , and our mission is to find the secret values that make both equations true! Watch out! Keep your calculations neat and organized, a tiny mistake with a plus or minus sign can throw everything off!

STEP 2

1. Elimination Setup
2. Solve for $x$
3. Solve for $y$

STEP 3

Let's multiply the first equation by 5 and the second equation by 7.
Why? Because we're setting the stage to eliminate $y$ !
This gives us: $5 \cdot (8x - 7y) = 5 \cdot (-3)$ $40x - 35y = -15$ and $7 \cdot (6x - 5y) = 7 \cdot (-1)$ $42x - 35y = -7$

STEP 4

Now, subtract the modified first equation from the modified second equation: $(42x - 35y) - (40x - 35y) = (-7) - (-15)$ $42x - 35y - 40x + 35y = -7 + 15$ $2x = 8$

STEP 5

Divide both sides of $2x = 8$ by 2 to isolate $x$ : $\frac{2x}{2} = \frac{8}{2}$ $x = 4$ We've found the first part of the puzzle! $x$ is 4!

STEP 6

Let's substitute our shiny new value of $x = 4$ back into the original first equation: $8 \cdot 4 - 7y = -3$ $32 - 7y = -3$

STEP 7

Subtract $32$ from both sides: $32 - 7y - 32 = -3 - 32$ $-7y = -35$

STEP 8

Divide both sides by $-7$ : $\frac{-7y}{-7} = \frac{-35}{-7}$ $y = 5$ Boom! We've cracked the code! $y$ is 5!

STEP 9

The solution to the system of equations is $x = 4$ and $y = 5$ !

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Questionems of Iline ar equations by 7. $\begin{array}{l} 8 x-7 y=-3 \\ 6 x-5 y=-1 \end{array}$

Studdy Solution

STEP 1

What is this asking? We've got two equations with two mystery numbers, $x$ and $y$ , and our mission is to find the secret values that make both equations true! Watch out! Keep your calculations neat and organized, a tiny mistake with a plus or minus sign can throw everything off!

STEP 2

1. Elimination Setup
2. Solve for $x$
3. Solve for $y$

STEP 3

Let's multiply the first equation by 5 and the second equation by 7.
Why? Because we're setting the stage to eliminate $y$ !
This gives us: $5 \cdot (8x - 7y) = 5 \cdot (-3)$ $40x - 35y = -15$ and $7 \cdot (6x - 5y) = 7 \cdot (-1)$ $42x - 35y = -7$

STEP 4

Now, subtract the modified first equation from the modified second equation: $(42x - 35y) - (40x - 35y) = (-7) - (-15)$ $42x - 35y - 40x + 35y = -7 + 15$ $2x = 8$

STEP 5

Divide both sides of $2x = 8$ by 2 to isolate $x$ : $\frac{2x}{2} = \frac{8}{2}$ $x = 4$ We've found the first part of the puzzle! $x$ is 4!

STEP 6

Let's substitute our shiny new value of $x = 4$ back into the original first equation: $8 \cdot 4 - 7y = -3$ $32 - 7y = -3$

STEP 7

Subtract $32$ from both sides: $32 - 7y - 32 = -3 - 32$ $-7y = -35$

STEP 8

Divide both sides by $-7$ : $\frac{-7y}{-7} = \frac{-35}{-7}$ $y = 5$ Boom! We've cracked the code! $y$ is 5!

STEP 9

The solution to the system of equations is $x = 4$ and $y = 5$ !

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Questionems of Iline ar equations by 7. 8x−7y=−36x−5y=−1\begin{array}{l} 8 x-7 y=-3 \\ 6 x-5 y=-1 \end{array}8x−7y=−36x−5y=−1​

Studdy Solution

STEP 1

What is this asking? We've got two equations with two mystery numbers, xxx and yyy, and our mission is to find the *secret values* that make both equations true! Watch out! Keep your calculations neat and organized, a tiny mistake with a plus or minus sign can throw everything off!

STEP 2

1. Elimination Setup2. Solve for xxx3. Solve for yyy

STEP 3

STEP 4

STEP 5

**Divide** both sides of 2x=82x = 82x=8 by **2** to isolate xxx: 2x2=82\frac{2x}{2} = \frac{8}{2}22x​=28​ x=4x = 4x=4We've found the first part of the puzzle! xxx is **4**!

STEP 6

Let's **substitute** our shiny new value of x=4x = 4x=4 back into the original first equation: 8⋅4−7y=−38 \cdot 4 - 7y = -38⋅4−7y=−3 32−7y=−332 - 7y = -332−7y=−3

STEP 7

**Subtract** 323232 from both sides: 32−7y−32=−3−3232 - 7y - 32 = -3 - 3232−7y−32=−3−32 −7y=−35-7y = -35−7y=−35

STEP 8

**Divide** both sides by −7-7−7: −7y−7=−35−7\frac{-7y}{-7} = \frac{-35}{-7}−7−7y​=−7−35​ y=5y = 5y=5Boom! We've cracked the code! yyy is **5**!

STEP 9

The solution to the system of equations is x=4x = 4x=4 and y=5y = 5y=5!

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Questionems of Iline ar equations by 7. $\begin{array}{l} 8 x-7 y=-3 \\ 6 x-5 y=-1 \end{array}$

What is this asking? We've got two equations with two mystery numbers, $x$ and $y$ , and our mission is to find the secret values that make both equations true! Watch out! Keep your calculations neat and organized, a tiny mistake with a plus or minus sign can throw everything off!

1. Elimination Setup
2. Solve for $x$
3. Solve for $y$

Divide both sides of $2x = 8$ by 2 to isolate $x$ : $\frac{2x}{2} = \frac{8}{2}$ $x = 4$ We've found the first part of the puzzle! $x$ is 4!

Let's substitute our shiny new value of $x = 4$ back into the original first equation: $8 \cdot 4 - 7y = -3$ $32 - 7y = -3$

Subtract $32$ from both sides: $32 - 7y - 32 = -3 - 32$ $-7y = -35$

Divide both sides by $-7$ : $\frac{-7y}{-7} = \frac{-35}{-7}$ $y = 5$ Boom! We've cracked the code! $y$ is 5!

The solution to the system of equations is $x = 4$ and $y = 5$ !