Answer :

GinnyAnswer
To solve the given system of equations:
[tex]\[ -5x - 2y = 7 \quad \text{(Equation 1)} \][/tex]
[tex]\[ 4x + 2y = 6 \quad \text{(Equation 2)} \][/tex]

we can follow these steps:

1. Add the equations to eliminate [tex]\(y\)[/tex]:
[tex]\[ (-5x - 2y) + (4x + 2y) = 7 + 6 \][/tex]
Simplifying the left side, we get:
[tex]\[ -x = 13 \][/tex]

Therefore, we solve for [tex]\(x\)[/tex]:
[tex]\[ -x = 13 \implies x = -13 \][/tex]

2. Substitute [tex]\(x = -13\)[/tex] back into one of the original equations to solve for [tex]\(y\)[/tex]:
We can use Equation 2 for this purpose:
[tex]\[ 4(-13) + 2y = 6 \][/tex]
Simplify and solve for [tex]\(y\)[/tex]:
[tex]\[ -52 + 2y = 6 \][/tex]
Add 52 to both sides:
[tex]\[ 2y = 58 \][/tex]
Now, divide by 2:
[tex]\[ y = 29 \][/tex]

3. Verify the solution by substituting [tex]\(x\)[/tex] and [tex]\(y\)[/tex] back into the original equations:
- For Equation 1:
[tex]\[ -5(-13) - 2(29) = 7 \][/tex]
Simplify:
[tex]\[ 65 - 58 = 7 \][/tex]
[tex]\[ 7 = 7 \][/tex]
- For Equation 2:
[tex]\[ 4(-13) + 2(29) = 6 \][/tex]
Simplify:
[tex]\[ -52 + 58 = 6 \][/tex]
[tex]\[ 6 = 6 \][/tex]

Since both equations are satisfied, the solution to the system is:
[tex]\[ x = -13 \quad \text{and} \quad y = 29 \][/tex]
Hi1315

Answer:

x = -13

y=29

Step-by-step explanation:

To solve the system of equations:

-5x - 2y = 7

4x + 2y = 6

1. Add the two equations to eliminate y:

(-5x - 2y) + (4x + 2y) = 7 + 6

-x = 13

x = -13

2. Substitute x = -13 into the second equation:

4(-13) + 2y = 6

-52 + 2y = 6

2y = 58

y=29

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