can someone answer this {2x + 6y = 20} {3x +4y = 10} using either substitution or elimination i need the “x” and “y” values.
The Correct Answer and Explanation is:
We can solve the system of equations using either substitution or elimination. Let’s use substitution in this case to solve for xxx and yyy.
The system of equations is:
- 2x+6y=202x + 6y = 202x+6y=20
- 3x+4y=103x + 4y = 103x+4y=10
Step 1: Solve for xxx in terms of yyy from the first equation.
From equation (1), solve for xxx:2x+6y=202x + 6y = 202x+6y=20
Subtract 6y6y6y from both sides:2x=20−6y2x = 20 – 6y2x=20−6y
Now divide both sides by 2:x=10−3yx = 10 – 3yx=10−3y
Step 2: Substitute x=10−3yx = 10 – 3yx=10−3y into the second equation.
Now substitute x=10−3yx = 10 – 3yx=10−3y into equation (2):3x+4y=103x + 4y = 103x+4y=10
Substitute for xxx:3(10−3y)+4y=103(10 – 3y) + 4y = 103(10−3y)+4y=10
Distribute the 3:30−9y+4y=1030 – 9y + 4y = 1030−9y+4y=10
Simplify:30−5y=1030 – 5y = 1030−5y=10
Now subtract 30 from both sides:−5y=10−30-5y = 10 – 30−5y=10−30−5y=−20-5y = -20−5y=−20
Divide both sides by -5:y=4y = 4y=4
Step 3: Substitute y=4y = 4y=4 into x=10−3yx = 10 – 3yx=10−3y.
Now that we know y=4y = 4y=4, substitute it back into x=10−3yx = 10 – 3yx=10−3y:x=10−3(4)x = 10 – 3(4)x=10−3(4)x=10−12x = 10 – 12x=10−12x=−2x = -2x=−2
Final Answer:
The solution to the system of equations is:x=−2andy=4x = -2 \quad \text{and} \quad y = 4x=−2andy=4
Explanation:
We first isolated xxx in terms of yyy from one equation, then substituted this expression into the second equation. This allowed us to solve for yyy, and once we found y=4y = 4y=4, we substituted this value back into the expression for xxx to find x=−2x = -2x=−2. Therefore, the solution to the system is x=−2x = -2x=−2 and y=4y = 4y=4.
