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zaharov [31]
3 years ago
11

Y= - x+2 Y=3x-4 Estimate the solution to the system of equations

Mathematics
1 answer:
IrinaVladis [17]3 years ago
8 0

Answer:

x=\frac{3}{2}\\ y=\frac{1}{2}

Step-by-step explanation:

y=-x+2\\y=3x-4

Let's solve one of them for x.

y=3x-4

Add 4

y+4=3x

Divide by 3.

x=\frac{y+4}{3}

Now, plug the value of y in the formula, or you can plug the value of x in the other equation. I'll take this one.

x=\frac{y+4}{3}

x=\frac{(-x+2)+4}{3}

x=\frac{-x+2+4}{3}

x=\frac{-x+6}{3}

Multiply by 3 to get rid of the denominator.

3x=-x+6

add x

3x+x=6

Combine like terms;

4x=6

Divide by 4.

x=\frac{6}{4}

Simplify.

x=\frac{3}{2}

Now that you found the value of x, replace it in any of the equations to find y.

y=-x+2\\y=-(\frac{3}{2})+2\\ y=-\frac{3}{2}+2

y=\frac{-3+2*2}{2} \\y=\frac{-3+4}{2} \\y=\frac{1}{2}

Proof:

y=3x-4\\\frac{1}{2}=3(\frac{3}{2})-4\\\frac{1}{2}=(\frac{9}{2})-4

\frac{1}{2}=\frac{9-4*2}{2}

\frac{1}{2}=\frac{9-8}{2}

\frac{1}{2}=\frac{1}{2}

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