The example on the left correctly uses SUBSTITUTION to solve a system. 1. Explain to yourself how each line of the example was derived.2. YOU TRY IT:Solve: y= 4xy=19−x
Question
The example on the left correctly uses SUBSTITUTION to solve a system. 1. Explain to yourself how each line of the example was derived.2. YOU TRY IT:Solve: y= 4xy=19−x
Solution
Sure, let's solve the system of equations step by step.
Given:
- y = 4x
- y = 19 - x
Step 1: Since both equations are equal to y, we can set them equal to each other. This is called the substitution method.
4x = 19 - x
Step 2: Solve for x. To do this, add x to both sides of the equation to get all x terms on one side.
4x + x = 19 5x = 19
Step 3: Divide both sides by 5 to solve for x.
x = 19/5 x = 3.8
Step 4: Substitute x = 3.8 into the first equation (y = 4x) to solve for y.
y = 4 * 3.8 y = 15.2
So, the solution to the system of equations is x = 3.8 and y = 15.2.
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