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3 years ago

Solve the system of equations.y= 2x + 4y = x2 + x - 2

Mathematics

1 answer:

bezimeni [28]3 years ago

3 0

Answer:

Step-by-step explanation:

$y=2x+4$

$y=x^2+x-2$

Both equations are solved for y so I'm just going to substitute

the 1st y (the 2x+4) into the second equation's y.

$2x+4=x^2+x-2$

I'm going to get everything on one side so I have 0=ax^2+bx+c.

Subtract 2x and subtract 4 on both sides:

$0=x^2-x-6$

Since the coefficient of x^2 is 1, all we have to do is find two numbers that multiply to be -6 and add up to be -1.

These numbers are -3 and 2.

So the factored form of our equation is:

$0=(x-3)(x+2)$

This means we have x-3=0 or x+2=0.

x-3=0

Add 3 on both sides:

x=3

x+2=0

Subtract 2 on both sides:

x=-2

So now we need to find y. I'm going to choose to use the easier equation:

y=2x+4.

If x=3, then y=2(3)+4=6+4=10. The ordered pair (3,10) is a solution.

If x=-2, then y=2(-2)+4=-4+4=0. The orded pair (-2,0) is a solution.

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Eli has saved $8 more than 1/3 of Angela's savings.If they each save $10 more Eli will have saved &4 more than Angela's savi

statuscvo [17]

Answer:

Eli has saved $10

Step-by-step explanation:

Let us use the first letters of their names to represent them.

A for Angela and E for ELi

So, from the first statement, we can write out an equation: E = $\frac{1}{3}$ A + 8, that is, one-third of Angela's savings + $8 will give us Eli's savings

From the second statement, we can write out: E + 10 = (A + 10) + 4 which means that if $10 is added to both their savings, Eli will still have $4 more than Angela.

So, we can solve both equations;

Equation 1: E = $\frac{1}{3}$ A + 8

Equation 2: E + 10 = (A + 10) + 4; which can be rewritten as E + 10 = A + 14

and then E = A + 4

The two equations (in bold), can then be solved simultaneously.

Let us carry out this operation to eliminate the E: Subtract equation 1 from equation 2, so that;

A + 4 - ( $\frac{1}{3}$ A + 8) = E - E

$\frac{2}{3}$ A - 4 = 0