Math  /  Algebra

QuestionFor the following exercises, use addition to solve the system of equations. 8. 8x+4y=26x5y=0.7\begin{array}{l} 8 x+4 y=2 \\ 6 x-5 y=0.7 \end{array}

Studdy Solution

STEP 1

What is this asking? We're trying to find the mystery numbers xx and yy that make both of these equations true at the same time! Watch out! Keep your calculations neat and organized, it's easy to get lost in the numbers!

STEP 2

1. Eliminate yy
2. Solve for xx
3. Solve for yy

STEP 3

Let's **multiply** the first equation by **5** and the second equation by **4**.
Why? Because this sets us up perfectly to eliminate the yy terms!
We're doing this so that the yy terms in both equations have the same *magnitude* but opposite *signs*.

STEP 4

5(8x+4y)=525 \cdot (8x + 4y) = 5 \cdot 2 40x+20y=1040x + 20y = 10

STEP 5

4(6x5y)=40.74 \cdot (6x - 5y) = 4 \cdot 0.7 24x20y=2.824x - 20y = 2.8

STEP 6

Now, let's **add** the modified equations together: (40x+20y)+(24x20y)=10+2.8(40x + 20y) + (24x - 20y) = 10 + 2.8 40x+24x+20y20y=12.840x + 24x + 20y - 20y = 12.864x=12.864x = 12.8

STEP 7

**Divide** both sides of the equation by **64** to isolate xx: 64x64=12.864\frac{64x}{64} = \frac{12.8}{64} x=0.2x = 0.2So, xx is **0.2**!

STEP 8

Now that we know x=0.2x = 0.2, we can **substitute** it back into either of the original equations.
Let's use the first one: 8(0.2)+4y=28(0.2) + 4y = 2 1.6+4y=21.6 + 4y = 2

STEP 9

**Subtract** 1.61.6 from both sides: 1.61.6+4y=21.61.6 - 1.6 + 4y = 2 - 1.6 4y=0.44y = 0.4

STEP 10

**Divide** both sides by **4** to find yy: 4y4=0.44\frac{4y}{4} = \frac{0.4}{4} y=0.1y = 0.1Awesome, yy is **0.1**!

STEP 11

We found x=0.2x = 0.2 and y=0.1y = 0.1!
These values satisfy both equations, solving our system!

Was this helpful?

Studdy solves anything!

banner

Start learning now

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

ParentsInfluencer programContactPolicyTerms
TwitterInstagramFacebookTikTokDiscord