solve the following system of equations enter the x coordinate of the solution. Round your answer to the nearest tenth. 5x+2y=22 -2x+6y=3
I would triple the first one:
15x + 6y = 66
-2x + 6y = 3
subtract them:
17x = 63
x = 63/17
back into original first:
5(63/17) + 2y = 22
2y = 59/17
y = 59/34
check them in the original equations, it works
To solve the system of equations:
1. Start by multiplying the first equation by 2 to eliminate the x coefficient in the second equation:
2 * (5x + 2y) = 2 * 22
This simplifies to:
10x + 4y = 44
2. Now we have two equations:
10x + 4y = 44
-2x + 6y = 3
3. Multiply the second equation by 5 to eliminate the x coefficient in the first equation:
5 * (-2x + 6y) = 5 * 3
This simplifies to:
-10x + 30y = 15
4. Now we have two equations:
10x + 4y = 44
-10x + 30y = 15
5. Add the two equations together to eliminate the x variables:
(10x + 4y) + (-10x + 30y) = 44 + 15
This simplifies to:
34y = 59
6. Solve for y by dividing both sides of the equation by 34:
y = 59/34 ≈ 1.74
7. Round the value of y to the nearest tenth:
y ≈ 1.7
8. Substitute the found value of y back into one of the original equations to solve for x. Let's use the first equation:
5x + 2(1.7) = 22
Simplify:
5x + 3.4 = 22
9. Subtract 3.4 from both sides of the equation:
5x = 22 - 3.4
This simplifies to:
5x = 18.6
10. Solve for x by dividing both sides of the equation by 5:
x = 18.6 / 5 ≈ 3.7
11. Round the value of x to the nearest tenth:
x ≈ 3.7
Therefore, the solution to the system of equations is (x, y) ≈ (3.7, 1.7).
To solve the given system of equations, you can use the method of substitution or the method of elimination. Here, I will explain how to solve it using the method of substitution:
Step 1: Start with the first equation: 5x + 2y = 22.
Solve this equation for x in terms of y.
5x = 22 - 2y
Divide both sides by 5:
x = (22 - 2y)/5
Step 2: Substitute the value of x (from Step 1) into the second equation: -2x + 6y = 3.
Replace x with (22 - 2y)/5 in the second equation.
-2((22 - 2y)/5) + 6y = 3
Step 3: Solve the equation obtained in Step 2 for y.
Multiply both sides of the equation by 5 to eliminate the fraction:
-2(22 - 2y) + 30y = 15
Distribute -2:
-44 + 4y + 30y = 15
Combine like terms:
34y - 44 = 15
Add 44 to both sides:
34y = 59
Divide both sides by 34 to isolate y:
y = 59/34
Step 4: Substitute the value of y back into the equation obtained in Step 1 to solve for x.
x = (22 - 2(59/34))/5
Simplify:
x = (22 - 118/34)/5
x = (22 - 3.4706)/5
x = 18.5294/5
x = 3.7059
Therefore, the solution to the given system of equations is x = 3.7 (rounded to the nearest tenth).