Step-by-step explanation:
Substitute y = 4 into the first equation:
[tex]4=2x^2+x-6[/tex]
Subtract 4 from both sides:
[tex]2x^2+x-10=0[/tex]
We can factor in order to find values of x.
Factor the equation:
[tex]2x^2+x-10=0[/tex]
Factors of 10 we'll use:
5 and 2.
[tex](2x+5)(x-2)=0[/tex]
Set the parentheses equal to 0 then find the values of x:
[tex](2x+5)=0[/tex]
[tex]x=-2\frac{1}{2}[/tex]
[tex](x-2)=0[/tex]
[tex]x=2[/tex]
[tex]x=2, \: or \: -2\frac{1}{2} .[/tex]
Check:
[tex]4=2(2)^2+2-6[/tex]
[tex]4=2(4)+2-6[/tex]
[tex]4=4 \: \checkmark[/tex]
[tex]4=2(-2\frac{1}{2} )^2-2\frac{1}{2} -6[/tex]
[tex]4=2(6\frac{1}{4})-2\frac{1}{2} -6[/tex]
[tex]4=12\frac{1}{2} -2\frac{1}{2} -6[/tex]
[tex]4=10-6[/tex]
[tex]4=4 \: \checkmark[/tex]
