Solve the system of equations using the graphing or substitution method. State your final answer as an ordered pair. DO NOT include spaces in your answer.y=2x−4𝑦=2𝑥−4y=4x−6𝑦=4𝑥−6Solution:
Question
Solve the system of equations using the graphing or substitution method. State your final answer as an ordered pair. DO NOT include spaces in your answer.y=2x−4𝑦=2𝑥−4y=4x−6𝑦=4𝑥−6Solution:
Solution 1
To solve the system of equations using the substitution method, we first set the two equations equal to each other because they both equal y:
2x - 4 = 4x - 6
Next, we solve for x:
2x = 4x - 6 + 4 2x = 4x - 2 2x - 4x = -2 -2x = -2 x = 1
Then we substitute x = 1 into the first equation to solve for y:
y = 2(1) - 4 y = 2 - 4 y = -2
So the solution to the system of equations is (1,-2).
Solution 2
To solve the system of equations using the substitution method, we first set the two equations equal to each other because they both equal y:
2x - 4 = 4x - 6
Next, we solve for x:
2x = 4x - 6 + 4 2x = 4x - 2 2x - 4x = -2 -2x = -2 x = 1
Then, we substitute x = 1 into the first equation to solve for y:
y = 2(1) - 4 y = 2 - 4 y = -2
So, the solution to the system of equations is (1,-2).
Solution 3
Step 1: Write down the given equations:
y = 2x - 4 y = 4x - 6
Step 2: Since both equations are equal to y, we can set them equal to each other:
2x - 4 = 4x - 6
Step 3: Solve for x:
Subtract 2x from both sides to get 2x = -2 Divide both sides by 2 to get x = -1
Step 4: Substitute x = -1 into the first equation to solve for y:
y = 2(-1) - 4 = -2 - 4 = -6
So, the solution to the system of equations is (-1,-6).
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